Question

There are 6 television shows coming on this week that Gabe wants to watch. They all come on at different times, but his mom will only let him watch 4 shows a week. How many different combinations of shows can Gabe choose to watch?
A.
15

B.
30

C.
45

D.
60

Answer 1

The correct answer is (A) .The problem asks for us to determine the different combinations of 4 shows from 6 shows.

This is a problem of choosing $r=4$ combinations from $n=6$ choices. To calculate the number of combinations of 4 objects from 6 objects ,we use the formula for calculating such combinations, i.e

$C(n,r)=\frac{n!}{r!(n-r)!} \\C(n,r)=\frac{6!}{4!(6-4)!} =\frac{6!}{4!2!} =\frac{6\times 5\times 4!}{4!\times 2!} =15.$

There are 15 combinations of shows that Gabe can make. The correct answer is (A)