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In how many ways can 22 distinct books be given to 5 students so that so that two students have 5 books each and another three students have 4 books each ?

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In how many ways can 22 distinct books be given to 5 students so that so that two students have 5 books each and another three students have 4 books each ?Question is about grouping and distribution.We have to make 2 groups of 5 and 3 groups of 4 and then distribute them to 5 students.No. of ways to group=22!5! 5! 4! 4! 4! 2! 3!=22!5!2 4!3 2! 3!No. of ways to distribute=22!5!2 4!3 2! 3!×5!=22!5! 4!3 2! 3! Answer

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  • 31
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I am not sure, yet I'll give it a try.
For the first student, no.of ways in which 5 books can be given is 22C5
Similarly, for the second, 17C5.( Since there are only 17 books remaining).
For the 3rd, 4th and 5th students, no.of ways of giving (distinct) books are 12C4, 8C4 and 4C4respectively.

So, the answer will be product of all these numbers.
n= 22C517C512C4 8C44C4
n= 5646383542800 ( Too big.. Thats why I am doubtful)

If wrong, someone tell me why..
  • -15
Thats why I mentioned the answer here
  • -5
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