Question

How many combinations of 7 candidates can fill 3 vacancies on a city council?

Answer 1

35 combinations

Explanation:

You have to use the formula for finding combinations in probability. It looks like this:

₇C₃ =
`(7!)/(3!(7-3)!)`

so that gives you

₇C₃ =
`(7*6*5*4!)/(3*2*1*4!)`

The 4 factorials cancel each other out, and when you do the math, you get 210/6. That divides evenly into 35. So there are 35 combinations.