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.
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?
1 answer
1 answer