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Question

12 different toys are to be distributed to three children equally. In how many ways this can be done?

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Solution

The 12 different toys are to be equally distributed among three children,so each children will get 123=4 toys
4 toys can be distributed among 3 people in:-
1st child will get 4 toys from 12 toys in 12C4 ways. Now 8 are remaining.
2nd child will get 4 toys from 8 toys in 8C4 ways.
3rd child will get 4 toys from 4 toys in only 1 way.
As above 4 events are occuring simultaneously .So they are to be multiplied with each other
12C4×8C4×1
=12!8!×4!×8!4!4!×1=34650

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