Question

The newly elected president needs to decide the remaining 66 spots available in the cabinet he/she is appointing. if there are 1111 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?

Answer 1

If the rank matters, we should use the permutation formula. The formula is nPk = n! / (n-k)!

Where n is the total number of people where k is how many people in must be in each group.

So in the problem n would be 11 and k would be 6.

nPk = n! divided by (n-k)!

= 11! Divided by 5!

= 332640

There are 332640 ways that the members of the cabinet can be appointed.