Question

The newly elected president needs to decide the remaining 6 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?

Answer 1

Answer: There are 151,200 ways the members can be appointed.

Step-by-step explanation:

Since we have given that

Number of eligible candidates = 10

Number of remaining spots available = 6

Here, rank matters.

so, we will use "Fundamental theorem of counting or by Permutation":

So, Number of different ways the members can be selected is given by

$^{10}P_6=10\times 9\times 8\times 7\times 6\times 5\\\\=151,200$

Hence, there are 151,200 ways the members can be appointed.