Question

There are 8 people on a basketball team, and the coach needs to choose 5 to put into a

game. How many different possible ways can the coach choose a team of 5 if each
person has an equal chance of being selected?

Answer 1

56 ways

Explanation:

From the question, the formula we can use is the combination formula

The combination formula is given as:

nCr = n!/r! (n-r)!

From the question, n = 8 and r = 5

8C5 = 8!/5! (8-5)!

= (8×7×6×5×4×3×2×1)/ (5×4×3×2×1)(3×2×1)

= 56 ways

Therefore, the different possible ways the coach can choose a team of 5 if each person has an equal chance of being selected is 56 ways.

Answer 2

There are 56 possible ways for the coach to choose the team.

Explanation:

The order in which the players are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In this question:

5 players from a set of 8. So

`C_(8,5) = (8!)/(5!(8-5)!) = 56`

There are 56 possible ways for the coach to choose the team.