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How many different ways can $18$ bottles are divided into $3$ groups of bottles for each team.
Option: 1
$2858856$

Option: 2
$23823$

Option: 3
$238200$

Option: 4
$238220$

Answers (1)

best_answer

The given information is:

Number of bottles $=18$

Number of groups $=3$

Number of bottles in each groups $=6$

Pick first $6$ bottles from $18$ bottles,

Total no. of ways of choosing is:

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

Pick next $6$ bottles from remaining $12$ bottles,

Total no. of ways of choosing is:

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

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

Since the three groups are similar, there is no differentiation between them. Therefore, we need to divide it with $3 !=6$ .

The total numbers of ways:

$\frac{18564 \times 924}{6}=2858856$

Posted by

Rishabh

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