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In how many ways 8 books can be divided into 4 children such that all contains 2 books to each child.

Option: 1

105


Option: 2

150


Option: 3

28


Option: 4

1820


Answers (1)

best_answer

The given information is:

Number of books =8

Number of children =4

Number of books to each child =2

Pick first 2 books from 8 books , 

Total no. of ways of choosing is:

\frac{8 !}{(8-2) ! 2 !}=\frac{8 !}{6 ! 2 !}=28

Pick next 2 books from 6 books ,

Total no. of ways of choosing is:

\frac{6 !}{(6-2) ! 2 !}=\frac{6 !}{4 ! 2 !}=15

Pick next 2 books from 4 books , 

Total no. of ways of choosing is:

\frac{4 !}{(4-2) ! 2 !}=\frac{4 !}{2 ! 2 !}=6

Pick last 2 books from remaining 2 books and the number of ways this can be done is 1 .

Since the five groups are similar, there is no differentiation between them. Therefore, we need to divide it with 4 !=24.

The total numbers of ways:

\frac{28 \times 15 \times 6}{24}=105

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