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In how many ways 6 balls can be divided into 3 children such that all contains 2 balls to each child.

Option: 1

20


Option: 2

150


Option: 3

15


Option: 4

6


Answers (1)

best_answer

The given information is:

Number of balls =6

Number of children =3

Number of  balls to each child =2

Pick first 2 balls from balls, 

Total no. of ways of choosing is:

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

Pick next 2 balls from 4 balls, 

Total no. of ways of choosing is:

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

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

Since the three groups are similar, there is no differentiation between them. Therefore, we need to divide it with  3 !=6.

The total numbers of ways:

\frac{15 \times 6}{6}=15

Posted by

manish painkra

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