Question

Find the number of different starting teams if 5 basketball players are chosen from a team of 12 players.

Answer 1

12C5

Answer 2

Can you explain?

Answer 3

For the first player you have 12 choices. For the second player, you have 11 choices (since you already chose one) so the number of ways to choose two players from a team of 12 is 12 · 11. By the same reasoning, (for the third player you have 10 choices, for the fourth player 9 choices and for the fifth player 8 choices) the number of different starting teams is\[12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 = 95040.\]

Answer 4

Well, I'm assuming the order that you use to choose the player matters (I have no idea how a basketball team is structured). If it doesn't you have to divide the result by the number of ways you can order 5 players, which is 5!, so the result would be\[\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8}{5!} = \frac{95040}{120} = 792.\]

Answer 5

LOL.