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In how many ways 14 toys can be divided into 2 groups such that all contains 7 toys to each.

Option: 1

3432


Option: 2

3430


Option: 3

1716


Option: 4

5775


Answers (1)

best_answer

The given information is:

Number of toys =14

Number of groups =2

Number of toys to each groups =7

Pick first 7 toys from 14 toys, 

Total no. of ways of choosing is:

\frac{14 !}{(14-7) ! 7 !}=\frac{14 !}{7 ! 7 !}=3432

Pick last 7 toys from 7 toys and the number of ways this can be done is 1 .

Since the two groups are similar, there is no differentiation between them. Therefore, we need to divide it with 2 !=2 .

The total numbers of ways:

\frac{3432}{2}=1716

Posted by

Rakesh

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