A cooperation must appoint a president, CEO, COO,and a CFO. It must also appoint a planning committee with 3 different members. There are 15 candidates and officers can also serve on the planning committee. How many different ways can the officers be appointed? How many ways can the committee members be appointed? What is the probability of randomly selecting the committee members and getting the 3 youngest of the candidates?

Question

A cooperation must appoint a president, CEO, COO,and a CFO. It must also appoint a planning committee with 3 different members. There are 15 candidates and officers can also serve on the planning committee. How many different ways can the officers be appointed? How many ways can the committee members be appointed? What is the probability of randomly selecting the committee members and getting the 3 youngest of the candidates?

Answer 1

To find the number of ways to appoint the officers, we can multiply the number of choices for each position.

Number of choices for the president = 15
Number of choices for the CEO = 14 (since one candidate has already been chosen as president)
Number of choices for the COO = 13 (as two candidates have already been chosen as president and CEO)
Number of choices for the CFO = 12 (as three candidates have already been chosen for the other positions)

Therefore, the number of ways to appoint the officers would be:
15 * 14 * 13 * 12 = 32,760 possible combinations.

To determine the number of ways to appoint the planning committee members, we need to consider that officers can also serve on the committee:

Number of choices for the first committee member = 15 (any of the 15 candidates)
Number of choices for the second committee member = 15 (any of the 15 candidates)
Number of choices for the third committee member = 15 (any of the 15 candidates)

Therefore, the number of ways to appoint the planning committee would be:
15 * 15 * 15 = 3,375 possible combinations.

To calculate the probability of randomly selecting the 3 youngest candidates for the committee, we need to consider the total number of possible outcomes (number of ways to appoint the committee) and the number of favorable outcomes (number of ways to select the 3 youngest candidates).

Number of favorable outcomes (selecting the 3 youngest candidates) = 1 (as there is only one way to select the youngest candidates)

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 3375
Probability ≈ 0.0002963 or 0.02963%