Question

There are six 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 four shows a week. How many different combinations of shows can Gabe watch?

a) 15
b) 24
c) 30
d) 60

Answer 1

By calculating the combinations using the formula C(6, 4), we find that Gabe can watch 15 different combinations of shows out of the six available. The correct answer is (a) 15.

Step-by-step explanation:

The question asks for the number of different combinations of television shows Gabe can watch given he can only watch four out of six shows. To solve this, we use the combinations formula which is C(n, r) = n! / (r!(n - r)!), where n represents the total number of items to choose from, and r represents how many items are being chosen.

In Gabe's case, n is 6 and r is 4. Plugging these into the formula, we get C(6, 4) = 6! / (4!(6 - 4)!). This simplifies to 6! / (4! * 2!), which further simplifies to (6 * 5 * 4 * 3) / (4 * 3 * 2), and after canceling out common factors, we are left with (6 * 5) / 2 = 15.

Therefore, Gabe can watch 15 different combinations of shows from the six available. The correct answer is (a) 15.