How many ways can you form a committee of 3 from a group of 10 people?

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Q: How many ways can you form a committee of 3 from a group of 10 people?

Solution: The number of ways to form a committee of 3 from 10 is given by 10C3 = 120.

Steps: 11

Step 1: Understand that we want to choose 3 people from a group of 10.
Step 2: Recognize that the order in which we choose the people does not matter (i.e., choosing Alice, Bob, and Charlie is the same as choosing Charlie, Bob, and Alice).
Step 3: Use the combination formula, which is written as nCr, where n is the total number of people and r is the number of people to choose. The formula is nCr = n! / (r! * (n - r)!).
Step 4: In our case, n = 10 and r = 3. So we need to calculate 10C3.
Step 5: Plug the numbers into the formula: 10C3 = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!).
Step 6: Calculate 10! = 10 × 9 × 8 × 7!, so we can cancel 7! in the numerator and denominator.
Step 7: Now we have 10C3 = (10 × 9 × 8) / (3 × 2 × 1).
Step 8: Calculate the numerator: 10 × 9 × 8 = 720.
Step 9: Calculate the denominator: 3 × 2 × 1 = 6.
Step 10: Divide the numerator by the denominator: 720 / 6 = 120.
Step 11: Therefore, there are 120 ways to form a committee of 3 from a group of 10 people.