a basketball team needs 5 players. the team can choose from a group of 7 players. explain how to find the combinations of players that can be on the team.
Ur sums kid
To find the combinations of players that can be on the team, you can use the concept of combinations. In this scenario, you have 7 players to choose from and want to form a team of 5 players.
Here's how you can calculate the combinations:
Step 1: Determine the number of players to choose (r = 5).
Step 2: Use the combination formula, which is represented as C(n, r) = n! / (r!(n-r)!), where n is the total number of players and r is the number of players to choose.
Step 3: Plug in the values into the formula:
C(7, 5) = 7! / (5!(7-5)!)
= 7! / (5!2!)
Step 4: Simplify the equation:
7! = 7 * 6 * 5! = 5040
5! = 5 * 4 * 3 * 2 * 1 = 120
2! = 2 * 1 = 2
C(7, 5) = 5040 / (120 * 2)
= 5040 / 240
= 21
Therefore, there are 21 different combinations of players that can be on the team.