Question

A youth soccer coach much choose 4 of his 9 players to go into a game.

In how many ways can this be done

Answer 1

The coach can select 4 out of 9 players in 126 different ways, calculated using the combination formula C(n, r) = n! / (r! * (n - r)!).

Step-by-step explanation:

To determine in how many ways the youth soccer coach can choose 4 out of his 9 players to go into a game, we can use the concept of combinations because the order in which the players are chosen does not matter. The number of combinations of n items taken r at a time is given by the formula:

C(n, r) = n! / (r! * (n - r)!)

Where:

• n is the total number of items.
• r is the number of items to choose.
• ! denotes factorial, the product of all positive integers up to that number.

For this scenario, n = 9 (total players) and r = 4 (players to choose), so the equation becomes:

C(9, 4) = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!) = (9*8*7*6) / (4*3*2*1) = 126

Therefore, the coach can choose the players in 126 different ways.