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Numbers of words which can be formed using all the letters of the word "AKSHI", if each word begins with vowel or terminates in vowel.
Correct answer is '84'. Can you explain this answer?
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Verified Answer
Numbers of words which can be formed using all the letters of the word...
Consider the words starting with A.
A−−−−
Number of ways of filling the 2nd place is 4
Number of ways of filling the 3rd place is 3
Number of ways of filling the 4th place is 2
Number of ways of filling the 5th place is 1
Hence in total 4×3×2×1=24
Similar cases for the words starting with I.=24
Hence 2×24 =48
Consider the words ending with A−−−−A
Number of ways of filling the 1st place is 4
Number of ways of filling the 2nd place is 3
Number of ways of filling the 3rd place is 2
Number of ways of filling the 4th place is 1
Hence in total 24 ways.
Similarly for I- 24 ways.
Hence total number of words 4×24=96
But this includes the words which start and end with Vowels.
Hence A−−−I
Number of such words is 3!.
Similarly I−−−A.
Number of such words is 3!.
Hence total number of words beginning with or ending with Vowels is
= 96−3!−3!=96−12
= 84
A−−−−
Number of ways of filling the 2nd place is 4
Number of ways of filling the 3rd place is 3
Number of ways of filling the 4th place is 2
Number of ways of filling the 5th place is 1
Hence in total 4×3×2×1=24
Similar cases for the words starting with I.=24
Hence 2×24 =48
Consider the words ending with A−−−−A
Number of ways of filling the 1st place is 4
Number of ways of filling the 2nd place is 3
Number of ways of filling the 3rd place is 2
Number of ways of filling the 4th place is 1
Hence in total 24 ways.
Similarly for I- 24 ways.
Hence total number of words 4×24=96
But this includes the words which start and end with Vowels.
Hence A−−−I
Number of such words is 3!.
Similarly I−−−A.
Number of such words is 3!.
Hence total number of words beginning with or ending with Vowels is
= 96−3!−3!=96−12
= 84
Most Upvoted Answer
Numbers of words which can be formed using all the letters of the word...
The number of words that can be formed using all the letters of a word can be found using the formula:
n!/(a!b!c!...),
where n is the total number of letters in the word, and a, b, c, etc. are the frequencies of each letter in the word.
For example, consider the word "hello". It has 5 letters, with the letter "l" appearing twice. Therefore, the number of words that can be formed using all the letters of "hello" is:
5!/(2!1!2!) = 60/(2x1x2) = 15.
Thus, there are 15 words that can be formed using all the letters of "hello".
n!/(a!b!c!...),
where n is the total number of letters in the word, and a, b, c, etc. are the frequencies of each letter in the word.
For example, consider the word "hello". It has 5 letters, with the letter "l" appearing twice. Therefore, the number of words that can be formed using all the letters of "hello" is:
5!/(2!1!2!) = 60/(2x1x2) = 15.
Thus, there are 15 words that can be formed using all the letters of "hello".
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Numbers of words which can be formed using all the letters of the word "AKSHI", if each word begins with vowel or terminates in vowel.Correct answer is '84'. Can you explain this answer?
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Numbers of words which can be formed using all the letters of the word "AKSHI", if each word begins with vowel or terminates in vowel.Correct answer is '84'. 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 Numbers of words which can be formed using all the letters of the word "AKSHI", if each word begins with vowel or terminates in vowel.Correct answer is '84'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Numbers of words which can be formed using all the letters of the word "AKSHI", if each word begins with vowel or terminates in vowel.Correct answer is '84'. Can you explain this answer?.
Numbers of words which can be formed using all the letters of the word "AKSHI", if each word begins with vowel or terminates in vowel.Correct answer is '84'. 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 Numbers of words which can be formed using all the letters of the word "AKSHI", if each word begins with vowel or terminates in vowel.Correct answer is '84'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Numbers of words which can be formed using all the letters of the word "AKSHI", if each word begins with vowel or terminates in vowel.Correct answer is '84'. Can you explain this answer?.
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