Question
The newly elected president needs to decide the remaining 5
spots available in the cabinet he/she is appointing. If there are 10
eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?
spots available in the cabinet he/she is appointing. If there are 10
eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?
Answers
GPT 3.5
The number of ways the 5 remaining spots in the cabinet can be filled by the 10 eligible candidates is given by the permutation formula:
P(n, r) = n! / (n - r)!
Where n is the total number of candidates (10 in this case) and r is the number of spots to be filled (5 in this case).
Therefore, the number of ways the 5 remaining spots can be filled is:
P(10, 5) = 10! / (10 - 5)!
= 10! / 5!
= 10 x 9 x 8 x 7 x 6
= 30,240
So, there are 30,240 different ways the members of the cabinet can be appointed.
P(n, r) = n! / (n - r)!
Where n is the total number of candidates (10 in this case) and r is the number of spots to be filled (5 in this case).
Therefore, the number of ways the 5 remaining spots can be filled is:
P(10, 5) = 10! / (10 - 5)!
= 10! / 5!
= 10 x 9 x 8 x 7 x 6
= 30,240
So, there are 30,240 different ways the members of the cabinet can be appointed.