Question

The newly elected president needs to decide the remaining 5 spots available in the cabinet he/she is appointing. If there are 15 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed

Answer 1

To calculate the number of different ways the members of the cabinet can be appointed, we can use the concept of permutations. Using the formula for permutations, it is found that there are 3003 different ways the members of the cabinet can be appointed.

Step-by-step explanation:

To calculate the number of different ways the members of the cabinet can be appointed, we can use the concept of permutations. Since there are 15 eligible candidates for the remaining 5 spots, and the order in which the members are appointed matters, we can use the formula for permutations:

P(n, r) = n! / (n - r)!

Where n is the total number of candidates and r is the number of spots available. In this case, we have:

P(15, 5) = 15! / (15 - 5)!

Calculating this gives us:

P(15, 5) = 15! / 10!

P(15, 5) = (15 × 14 × 13 × 12 × 11) / (5 × 4 × 3 × 2 × 1)

P(15, 5) = 3003

Therefore, there are 3003 different ways the members of the cabinet can be appointed.

Answer 2

Answer: There are 360360 ways to appoint the members of the cabinet.

Step-by-step explanation:

Since we have given that

Number of eligible candidates = 15

Number of spots available = 5

We need to find the number of different ways the members can be appointed where rank matters

For this we will use "Permutations":

So, the required number of different ways in choosing the members for appointment is given by

`^(15)P_5=360360`

Hence, there are 360360 ways to appoint the members of the cabinet.