Question

The newly elected president needs to decide the remaining 7 spots available in the cabinet he/she is appointing. If there are 12 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?

Answer 1

Answer: The total number of ways are 792 ways.

Explanation:

The total number of spots available is 7.

The total number of eligible candidate is 12.

To find the number of combinations we have a combination formula.

$^nC_r=\frac{n!}{r!(n-r)!}$

Where n is total number of of objects and r is the number of selected objects.

Since we have to select 7 spots from 12 candidates, therefore the total number of ways is calculated as shown below,

$^{12}C_7=\frac{12!}{7!(12-7)!}$

$^{12}C_7=\frac{12\times 11\times 10\times 9\times 8\times7!}{7!5!}$

$^{12}C_7=\frac{12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2\times 1}$

$^{12}C_7=792$

Therefore, the total number of ways are 792 ways.