Question

a baking club wants to form an executive committee. there are $12$ people in the baking club, including mark. in how many ways can the baking club form an executive committee with $5$ people, not including mark?

Answer 1

To form an executive committee without Mark, there are 11 people to choose from. Using combinations, the number of ways to create a 5-person committee from the 11 available is 462.

Step-by-step explanation:

The question involves a combinatorial problem where we need to select a committee from a group of people, which is a common type of problem in probability and statistics. We use the combination formula to calculate the number of ways to choose a committee of a certain size from a larger group. Specifically, the formula for combinations is given by C(n, k) = n! / (k!(n-k)!), where n is the total number of people to choose from, k is the number of people to be chosen, and ! denotes the factorial of a number.

For this particular problem, excluding Mark, there are 11 candidates available to form a 5-member executive committee. Therefore, we calculate the number of ways to pick 5 out of the 11 members using the combination formula. This can be calculated as follows: C(11, 5) = 11! / (5! * (11-5)!) = 11! / (5! * 6!) = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1) = 462 ways.