SOLUTION: In how many ways could 15 people be divided into five groups containing, respectively, 1 ,5,2,4, and 3 people ?

Question 1209207: In how many ways could 15 people be divided into five groups containing, respectively, 1 ,5,2,4, and 3 people ?

Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.
In how many ways could 15 people be divided into five groups containing,
respectively, 1, 5, 2, 4, and 3 people ?
~~~~~~~~~~~~~~~

One person from 15 persons for the 1st group can be selected in   = 15 ways. 

5 persons from 14 remaining persons for the 2nd group can be selected in   = 2002 ways. 

2 persons from  9 remaining persons for the 3rd group can be selected in    =   36 ways. 

4 persons from  7 remaining persons for the 4th group can be selected in    =   35 ways. 

3 persons from  3 remaining persons for the 5th group can be selected in    =    1 way. 


The total number of ways to create 5 different groups as described and requested is  15*2002*36*35*1 = 37837800.

Solved.

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