If a team of 4 is to be selected from 8 players, how many different teams can be
Practice Questions
Q1
If a team of 4 is to be selected from 8 players, how many different teams can be formed?
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Questions & Step-by-Step Solutions
If a team of 4 is to be selected from 8 players, how many different teams can be formed?
Step 1: Understand that we need to choose 4 players from a total of 8 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 this case, n = 8 and r = 4, so we need to calculate 8C4.
Step 6: Plug the values into the formula: 8C4 = 8! / (4! * (8 - 4)!) = 8! / (4! * 4!).
Step 7: Calculate 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, but since we have 4! in the denominator, we can simplify it: 8C4 = (8 × 7 × 6 × 5) / (4 × 3 × 2 × 1).
