Question

In how many ways can two basketball, 3 volleyballs and 4 soccer balls be arranged in a rack with 9 slots?​

Answer 1

Answer:

81 ways

Step-by-step explanation:

Answer 2

Permutation and Combination

Total 9 slots are given.

There are 2 basketballs, 3 volleyballs, 4 soccer balls.

Total number of all balls $=2+3+4=9\ balls$

Number of ways of arrangement of keeping these balls in given slots/racks$= \frac{9!}{2!\times 3!\times4!}$

$=1260 \ ways$

So, this arrangement can be done in 1260 ways.

It is considered as 2 basketballs are alike, 3 volleyballs are alike, 4 soccer balls are alike. So, to overcome the repetitiveness , we need to de-permute the alike kind, so denominator part was written there.