Question

There are 19 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

To calculate the number of different possible ways the coach can choose a team of 5 players from a group of 19, we use the concept of combination. Applying the formula nCr = n! / ((n-r)! * r!), we find that there are 116,280 different possible ways the coach can choose a team.

Step-by-step explanation:

To calculate the number of different possible ways the coach can choose a team of 5 players out of 19, we use the concept of combination. The formula for combination is nCr = n! / ((n-r)! * r!), where n is the total number of players and r is the number of players to be selected.

Applying this formula, we have 19C5 = 19! / ((19-5)! * 5!). Simplifying this expression, we get 19C5 = (19 * 18 * 17 * 16 * 15) / (5 * 4 * 3 * 2 * 1).

Calculating this expression, we find that 19C5 = 116,280. Therefore, there are 116,280 different possible ways the coach can choose a team of 5 players.