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

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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) About Me  (Show Source):
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In how many ways could 15 people be divided into five groups containing,
respectively, 1, 5, 2, 4, and 3 people ?
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One person from 15 persons for the 1st group can be selected in  C%5B15%5D%5E1 = 15 ways. 

5 persons from 14 remaining persons for the 2nd group can be selected in  C%5B14%5D%5E5 = 2002 ways. 

2 persons from  9 remaining persons for the 3rd group can be selected in  C%5B9%5D%5E2  =   36 ways. 

4 persons from  7 remaining persons for the 4th group can be selected in  C%5B7%5D%5E4  =   35 ways. 

3 persons from  3 remaining persons for the 5th group can be selected in  C%5B3%5D%5E3  =    1 way. 


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

Solved.