**Contents**show

## How many different ways can a coach choose three players from 8 bench players to replace three of the five starting players of a basketball team?

First notice that 8 choose 5 is the same as 8 choose 3 since choosing five players to be on the court is equivalent to choosing 3 players to sit on the bench. I’m going to work with 8 choose 3 since it is easier. **6 ways**.

## How many different combinations are possible if 3 players are selected from a team of 9?

In the end, we see that there are **84 ways** to pick 3 people from a group of 9 as long as order does not matter. Consider another example.

## How many ways can a team of 5 players be chosen from 8 players?

if none of them is selected then there is only one combination of 8–3=5 persons. 2. In all other case we want all three , so assuming them one , we have 5 other persons and we have to select 20 out of them. So such combinations will be 5c2=5*4/(2*1)=10, hence total options are=10+**1=11**.

Combination: Choosing 3 desserts from a menu of 10. C(10,3) = 120. Permutation: Listing your 3 favorite desserts, in order, from a menu of 10. P(10,3) = **720**.

## How many ways can the first second and third place be chosen from 10 contestants?

There are **720 different outcomes** possible in the race.

## How many ways can 5 basketball players?

The number of ways in which 5 basketball players can be selected from 8 basketball players is 8C5=56 8 C 5 = 56 . Using the product rule, the total number of ways in which both these selections can be made is 330∗56=**18480** 330 ∗ 56 = 18480 .