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The first name of a person consist of 9 letters in which letter occurs more than one and the other letters of are different. If the number of permutations of the letters of his name taken all at a time be 15120, then find the number of times the like letter occurs.?
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The first name of a person consist of 9 letters in which letter occurs...
Let that particular number be repeated "n" times. Then the number of possible permutations equal s,
9!/n! = 15120
n! = 9!/15120 = 24
=> n = 4 (since 4! = 24)
That particular letter is repeated 4 times
Community Answer
The first name of a person consist of 9 letters in which letter occurs...
Given:
The first name of a person consists of 9 letters.
The number of permutations of the letters of his name taken all at a time is 15120.

To Find:
The number of times the duplicate letter occurs.

Approach:
1. Let's assume that the duplicate letter occurs 'x' times in the name.
2. Since the name consists of 9 letters, the remaining (9 - x) letters are all different.
3. The number of permutations of the letters can be calculated using the formula:
P(n, k) = n! / (n - k)!
where n is the total number of letters and k is the number of times the duplicate letter occurs.
In this case, P(9, x) = 15120.
4. We can solve the above equation to find the value of 'x'.

Solution:
1. P(9, x) = 9! / (9 - x)! = 15120
2. Simplifying the equation, we get:
9! / (9 - x)! = 15120
9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (9 - x)! = 15120
362880 / (9 - x)! = 15120
3. We can rewrite 15120 as 10! / (10 - x)!:
362880 / (9 - x)! = 10! / (10 - x)!
4. Cross-multiplying, we get:
362880 * (10 - x)! = 10! * (9 - x)!
5. Dividing both sides by 10!, we get:
(10 - x)! = 362880 / (9 - x)!
6. Simplifying further:
(10 - x)! = 40320 / (9 - x)!
7. Looking at the factorials, we can see that (10 - x)! is one less than 10!, and (9 - x)! is one less than 9!.
8. Therefore, we can rewrite the equation as:
9! = 40320
9. Solving for 9!, we find that 9! = 362880.
10. Comparing the value of 9! with 40320, we can see that they are not equal.
11. Thus, there is no solution to the equation, and it is not possible to find the number of times the duplicate letter occurs.

Conclusion:
Based on the given information and calculations, it is not possible to determine the number of times the duplicate letter occurs in the person's name.
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The first name of a person consist of 9 letters in which letter occurs more than one and the other letters of are different. If the number of permutations of the letters of his name taken all at a time be 15120, then find the number of times the like letter occurs.?
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The first name of a person consist of 9 letters in which letter occurs more than one and the other letters of are different. If the number of permutations of the letters of his name taken all at a time be 15120, then find the number of times the like letter occurs.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The first name of a person consist of 9 letters in which letter occurs more than one and the other letters of are different. If the number of permutations of the letters of his name taken all at a time be 15120, then find the number of times the like letter occurs.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first name of a person consist of 9 letters in which letter occurs more than one and the other letters of are different. If the number of permutations of the letters of his name taken all at a time be 15120, then find the number of times the like letter occurs.?.
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