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In how many ways $12$ flowers can be divided into $4$ children such that all contains $3$ flowers to each child.
Option: 1
$220$

Option: 2
$150$

Option: 3
$1540$

Option: 4
$15400$

Answers (1)

best_answer

The given information is:

Number of flowers $=12$

Number of children $=4$

Number of flowers to each child $=3$

Pick first $3$ flowers from $12$ flowers,

Total no. of ways of choosing is:

$\frac{12 !}{(12-3) ! 3 !}=\frac{12 !}{9 ! 3 !}=220$

Pick next $3$ flowers from $9$ flowers,

Total no. of ways of choosing is:

$\frac{9 !}{(9-3) ! 3 !}=\frac{9 !}{6 ! 3 !}=84$

Pick next $3$ flowers from $6$ flowers,

Total no. of ways of choosing is:

$\frac{6 !}{(6-3) ! 3 !}=\frac{6 !}{3 ! 3 !}=20$

Pick last $3$ flowers from remaining $3$ flowers 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:

$\frac{220 \times 84 \times 20}{24}=15400$

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