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
To find the number of different combinations of shows Gabe can choose to watch, we can use the formula for combinations.
The number of combinations of n objects taken r at a time is given by nCr = n! / (r!(n-r)!), where ! denotes factorial.
In this case, Gabe wants to watch 4 shows out of 6, so n = 6 (the number of shows) and r = 4 (the number of shows he wants to watch).
Plugging in the values, we have 6C4 = 6! / (4!(6-4)!) = 6! / (4!2!) = (6 * 5 * 4 * 3!) / (4 * 3!) = (6 * 5) / 2 = 30.
Therefore, there are 30 different combinations of shows that Gabe can choose to watch.
So the answer is b. 30.