Question

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

Answer 1

Answer:

35 combinations

Step-by-step explanation:

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

₇C₃ = $\frac{7!}{3!(7-3)!}$

so that gives you

₇C₃ = $\frac{7*6*5*4!}{3*2*1*4!}$

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.