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  • In how many ways can 14 diamonds be divided into 3 groups in such a way that they get one, four and nine diamonds?Option: 1 <img alt="10010

In how many ways can 14 diamonds be divided into 3 groups in such a way that they get one, four and nine diamonds?

Option: 1

100100


Option: 2

960960


Option: 3

240260


Option: 4

10010


Answers (1)

best_answer

Number of ways of dividing (m+n+p) \text { (where } m \neq n \neq p \text ) things into three unequal

groups of size m,n,p is =\frac{(m+n+p) !}{m ! n ! p !}

Here m=1, n=4, p=9

Then, the total number of ways: 

\frac{14 !}{1 ! 4 ! 9 !}=10010

Posted by

sudhir.kumar

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