JEE Exam > JEE Questions > Find the probability that in a random arrang...
Start Learning for Free
Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.
- a)4/5
- b)1/5
- c)3/5
- d)2/3
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Find the probability that in a random arrangement of letter of the wo...
Out of theTetters in the word ‘UNIVERSITY’ two letters ‘I’ are alike.
View all questions of this test
∴ Number of permutations = 10!/2 …(i)
Number of words in which two ‘I’ are never together = Total number of words - Number of words in which two ‘I’ are together
∴ Required probability = 
= 8/10 = ⅘.
Most Upvoted Answer
Find the probability that in a random arrangement of letter of the wo...
Probability of two 'I's not coming together in the word "UNIVERSITY"
- The word "UNIVERSITY" has 10 letters in total.
- There are 2 'I's in the word.
Total number of arrangements
- The total number of arrangements of the letters in the word "UNIVERSITY" is 10!/(3!2!) = 30,240.
Number of arrangements where two 'I's come together
- Consider the two 'I's as a single entity.
- Now, we have 9 entities (UNVERSITY + II) to arrange, which can be done in 9!/(3!) = 30,240 ways.
Number of arrangements where two 'I's do not come together
- Subtract the arrangements where two 'I's come together from the total arrangements: 30,240 - 30,240 = 0.
Probability
- Probability of two 'I's not coming together = Number of arrangements where two 'I's do not come together / Total number of arrangements
- Probability = 0 / 30,240 = 0
- Simplifying, we get 0/1 = 0.
Therefore, the probability that in a random arrangement of the word "UNIVERSITY", two 'I's do not come together is 0, which is equivalent to 0/1 or 0%. Hence, option 'A' (4/5) is incorrect, and the correct answer is option 'A' (0).
- The word "UNIVERSITY" has 10 letters in total.
- There are 2 'I's in the word.
Total number of arrangements
- The total number of arrangements of the letters in the word "UNIVERSITY" is 10!/(3!2!) = 30,240.
Number of arrangements where two 'I's come together
- Consider the two 'I's as a single entity.
- Now, we have 9 entities (UNVERSITY + II) to arrange, which can be done in 9!/(3!) = 30,240 ways.
Number of arrangements where two 'I's do not come together
- Subtract the arrangements where two 'I's come together from the total arrangements: 30,240 - 30,240 = 0.
Probability
- Probability of two 'I's not coming together = Number of arrangements where two 'I's do not come together / Total number of arrangements
- Probability = 0 / 30,240 = 0
- Simplifying, we get 0/1 = 0.
Therefore, the probability that in a random arrangement of the word "UNIVERSITY", two 'I's do not come together is 0, which is equivalent to 0/1 or 0%. Hence, option 'A' (4/5) is incorrect, and the correct answer is option 'A' (0).
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
|
|
Top Courses for JEEView all
Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. Can you explain this answer?
Question Description
Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. 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 Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. Can you explain this answer?.
Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. 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 Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. Can you explain this answer?.
Solutions for Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. 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 Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Find the probability that in a random arrangement of letter of the words “UNIVERSITY” two ‘I’s do not come together.a)4/5b)1/5c)3/5d)2/3Correct answer is option 'A'. 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup