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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:

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

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