Keeping people in the rooms!

For discussing Olympiad Level Combinatorics problems
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samiul_samin
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Keeping people in the rooms!

Unread post by samiul_samin » Thu Feb 15, 2018 11:27 am

In how many ways you can keep $10$ people in $5$ rooms?

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samiul_samin
Posts: 1007
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Re: Keeping people in the rooms!

Unread post by samiul_samin » Mon Feb 19, 2018 1:31 pm

Solved this in my own.
Hint
Use Ball in urn formula
Answer
$\fbox{10!× 126}$
Problem Source
'বিজ্ঞানচিন্তা' January 2018
Solution
Let the peoples are $10$ different types of ball and the rooms are $5$ same urns
Using Ball and urn formula
We can put 10 identical ball in 5 urn $\dbinom 94=126$ ways
If they all are different balls then they can be permuted in $10!$ ways.
So,the total ways of permutation is $\fbox {10!×126}$
The answer is $\fbox {10!×126}$

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