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 [tex]r=4[/tex] combinations from [tex]n=6[/tex] choices. To calculate the number of combinations of 4 objects from 6 objects ,we use the formula for calculating such combinations, i.e
[tex]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.[/tex]
There are 15 combinations of shows that Gabe can make. The correct answer is (A)
