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In how many ways 24 men can be divided into 4 sides such that all contain 6 men to each.

Option: 1

92300


Option: 2

96197645544


Option: 3

18564


Option: 4

92378


Answers (1)

best_answer

The given information is:

Number of men =24

Number of sides =4

Number of men to each side =6

Pick first 6 men from 24 men, 

Total no. of ways of choosing is:

\frac{24 !}{(24-6) ! 6 !}=\frac{24 !}{18 ! 6 !}=134596

Pick first 6 men from 18 men, 

Total no. of ways of choosing is:

\frac{18 !}{(18-6) ! 6 !}=\frac{18 !}{12 ! 6 !}=18564

Pick first 6 men from 12 men, 

Total no. of ways of choosing is:

\frac{12 !}{(12-6) ! 6 !}=\frac{12 !}{6 ! 6 !}=924

Pick last 6 men from 6 men and the number of ways this can be done is 1 .

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

The total numbers of ways:

\frac{134596 \times 18564 \times 924}{24}=96197645544

Posted by

seema garhwal

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