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How many ways $16$ people can be divided into $4$ groups, such that all four of them contain $4$ people each.
Option: 1
$2627600$

Option: 2
$2627625$

Option: 3
$262762$

Option: 4
$262760$

Answers (1)

best_answer

The given information is:

Number of people $=16$

Number of groups $=4$

Number of people in all groups $=4$

Pick first $4$ people from $16$ people,

Total no. of ways of choosing is:

$\frac{16 !}{(16-4) ! 4 !}=\frac{16 !}{12 ! 4 !}=1820$

Pick next $4$ people from $12$ people,

Total no. of ways of choosing is:

$\frac{12 !}{(12-4) ! 4 !}=\frac{12 !}{8 ! 4 !}=495$

Pick next $4$ people from $8$ people,

Total no. of ways of choosing is:

$\frac{8 !}{(8-4) ! 4 !}=\frac{8 !}{4 ! 4 !}=70$

Pick last $4$ people from $4$ people 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 $4 !=24$ .

$\frac{1820 \times 495 \times 70}{24}=2627625$

Posted by

Ritika Jonwal

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