If a committee of 3 members is to be formed from a group of 5 people, how many different committees can be formed?

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Q: If a committee of 3 members is to be formed from a group of 5 people, how many different committees can be formed?

Solution: The number of ways to choose 3 members from 5 is given by 5C3 = 10.

Steps: 9

Step 1: Understand that we need to choose 3 members from a group of 5 people.
Step 2: Recognize that this is a combination problem, where 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 (5 people) and r is the number of items to choose (3 members).
Step 4: The combination formula is nCr = n! / (r! * (n - r)!), where '!' denotes factorial, which is the product of all positive integers up to that number.
Step 5: Plug in the values: 5C3 = 5! / (3! * (5 - 3)!) = 5! / (3! * 2!).
Step 6: Calculate the factorials: 5! = 5 × 4 × 3 × 2 × 1 = 120, 3! = 3 × 2 × 1 = 6, and 2! = 2 × 1 = 2.
Step 7: Substitute the factorials back into the formula: 5C3 = 120 / (6 * 2) = 120 / 12.
Step 8: Simplify the calculation: 120 / 12 = 10.
Step 9: Conclude that there are 10 different committees that can be formed.