a) To find the number of ways the baking club can form an executive committee with 2 people, we need to choose 2 people out of the 12 people. This can be done in mathematical notation as 12C2.
Using the formula for combinations, 12C2 = 12! / (2! * (12-2)!)
Simplifying this expression, we get: 12! / (2! * 10!)
Since 2! = 2, this further simplifies to: 12 * 11 / 2
Therefore, there are 66 ways the baking club can form an executive committee with 2 people.
b) Since Mark must be included in the executive committee, we only need to choose 1 more person from the remaining 11 people. This can be done in mathematical notation as 11C1.
Using the formula for combinations, 11C1 = 11! / (1! * (11-1)!)
Simplifying this expression, we get: 11! / (1! * 10!)
Since 1! = 1, this further simplifies to: 11 * 1
Therefore, there are 11 ways the baking club can form an executive committee with 2 people, including Mark.
c) To form an executive committee with 2 people, not including Mark, we need to choose 2 people from the remaining 11 people (excluding Mark). This can be done in mathematical notation as 11C2.
Using the formula for combinations, 11C2 = 11! / (2! * (11-2)!)
Simplifying this expression, we get: 11! / (2! * 9!)
Since 2! = 2, this further simplifies to: 11 * 10 / 2
Therefore, there are 55 ways the baking club can form an executive committee with 2 people, not including Mark.
a) 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 2 people?
b) 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 2 people, including Mark?
c) 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 2 people, not including Mark?
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