If a team of 5 is to be selected from 10 players, how many different teams can b

If a team of 5 is to be selected from 10 players, how many different teams can be formed?

If a team of 5 is to be selected from 10 players, how many different teams can be formed?

Step 1: Understand that we need to choose 5 players from a total of 10 players.
Step 2: Recognize that this is a combination problem because the order of selection does not matter.
Step 3: Use the combination formula, which is written as nCr, where n is the total number of items (players) and r is the number of items to choose (players to select).
Step 4: The formula for combinations is nCr = n! / (r! * (n - r)!), where '!' denotes factorial, which is the product of all positive integers up to that number.
Step 5: In our case, n = 10 and r = 5. So we need to calculate 10C5.
Step 6: Plug the values into the formula: 10C5 = 10! / (5! * (10 - 5)!) = 10! / (5! * 5!).
Step 7: Calculate 10! (10 factorial) which is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.
Step 8: Calculate 5! (5 factorial) which is 5 x 4 x 3 x 2 x 1.
Step 9: Substitute the factorial values back into the equation: 10C5 = (10 x 9 x 8 x 7 x 6) / (5 x 4 x 3 x 2 x 1).
Step 10: Simplify the calculation to find the total number of different teams that can be formed, which equals 252.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – The formula used to determine the number of ways to choose a subset of items from a larger set, denoted as nCr.