Final answer:
To determine how many ways a coach can choose five starters from 12 players, we use the combinations formula. There are 792 different ways the coach can choose the five starters.
Step-by-step explanation:
To determine how many ways a coach can choose five starters from a team of 12 players, we need to use the concept of combinations. This is because the order in which the players are chosen does not matter. The formula for combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of players, and k is the number of starters to choose.
In this case, n = 12 and k = 5. So, the number of ways the coach can choose the starters is:
C(12, 5) = 12! / (5!(12-5)!) =
12! / (5!7!) =
(12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1) =
(12 × 11 × 2 × 9 × 8) / (1) =
95040 / 120 =
792.
There are 792 different ways in which the coach can choose the five starters from a team of 12 players.