JEE Exam > JEE Questions > (i) Find the number of four letter word that ...
Start Learning for Free
(i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)
(ii) How many of them contain only consonants?
(iii) How many of them begin & end in a consonant?
(iv) How many of them begin with a vowel?
(v) How many contain the letters Y?
(vi) How many begin with T & end in a vowel?
(vii) How many begin with T & also contain S?
(viii) How many contain both vowels?
- a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240
- b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240
- c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
(i) Find the number of four letter word that can be formed from the le...
Most Upvoted Answer
(i) Find the number of four letter word that can be formed from the le...
With a vowel and end with a consonant?
(i) To find the number of four-letter words that can be formed from the letters of the word "HISTORY," we can use the concept of permutations. Since each letter can only be used at most once, we need to select 4 out of the 7 available letters. This can be done in 7P4 ways.
7P4 = 7! / (7-4)! = 7! / 3! = 7 * 6 * 5 * 4 = 840
Therefore, there are 840 four-letter words that can be formed from the letters of the word HISTORY.
(ii) To find the number of four-letter words that contain only consonants, we need to consider the consonants in the word HISTORY. The consonants in the word HISTORY are H, S, T, and R. We need to select 4 out of these 4 consonants, which can be done in 4P4 ways.
4P4 = 4! / (4-4)! = 4! / 0! = 4 * 3 * 2 * 1 = 24
Therefore, there are 24 four-letter words that contain only consonants.
(iii) To find the number of four-letter words that begin with a vowel and end with a consonant, we need to consider the vowels and consonants in the word HISTORY. The vowels in the word HISTORY are I and O, and the consonants are H, S, T, and R.
The number of four-letter words that begin with a vowel and end with a consonant can be found by multiplying the number of choices for the first letter (2 vowels) by the number of choices for the second letter (5 letters, since we can choose from all the letters except the first letter), by the number of choices for the third letter (4 letters, since we can choose from all the letters except the first and last letters), and finally by the number of choices for the last letter (4 consonants).
2 * 5 * 4 * 4 = 160
Therefore, there are 160 four-letter words that begin with a vowel and end with a consonant.
(i) To find the number of four-letter words that can be formed from the letters of the word "HISTORY," we can use the concept of permutations. Since each letter can only be used at most once, we need to select 4 out of the 7 available letters. This can be done in 7P4 ways.
7P4 = 7! / (7-4)! = 7! / 3! = 7 * 6 * 5 * 4 = 840
Therefore, there are 840 four-letter words that can be formed from the letters of the word HISTORY.
(ii) To find the number of four-letter words that contain only consonants, we need to consider the consonants in the word HISTORY. The consonants in the word HISTORY are H, S, T, and R. We need to select 4 out of these 4 consonants, which can be done in 4P4 ways.
4P4 = 4! / (4-4)! = 4! / 0! = 4 * 3 * 2 * 1 = 24
Therefore, there are 24 four-letter words that contain only consonants.
(iii) To find the number of four-letter words that begin with a vowel and end with a consonant, we need to consider the vowels and consonants in the word HISTORY. The vowels in the word HISTORY are I and O, and the consonants are H, S, T, and R.
The number of four-letter words that begin with a vowel and end with a consonant can be found by multiplying the number of choices for the first letter (2 vowels) by the number of choices for the second letter (5 letters, since we can choose from all the letters except the first letter), by the number of choices for the third letter (4 letters, since we can choose from all the letters except the first and last letters), and finally by the number of choices for the last letter (4 consonants).
2 * 5 * 4 * 4 = 160
Therefore, there are 160 four-letter words that begin with a vowel and end with a consonant.
Free Test
FREE
| Start Free Test |
Community Answer
(i) Find the number of four letter word that can be formed from the le...
A.7P4
B.5P4
B.5P4
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
(i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer?
Question Description
(i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
(i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
Solutions for (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
(i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice (i) Find the number of four letter word that can be formed from the letters of the word HISTORY. (each letter to be used at most once)(ii) How many of them contain only consonants?(iii) How many of them begin & end in a consonant?(iv) How many of them begin with a vowel?(v) How many contain the letters Y?(vi) How many begin with T & end in a vowel?(vii) How many begin with T & also contain S?(viii) How many contain both vowels?a)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 200 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240b)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 480 ; (v) 240 ; (vi) 40 ; (vii) 60 ; (viii) 240c)(i) 840 ; (ii) 120 ; (iii) 400 ; (iv) 240 ; (v) 480 ; (vi) 40 ; (vii) 60 ; (viii) 240d)None of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup