Question

You have the first season of your favorite television show on a set of DVDs. The set
contains 10 episodes. You have time to watch 2 episodes. How many combinations
of 2 episodes can you watch?

Answer 1

Answer: There are 45 combinations.

Step-by-step explanation:

If the order in which you watch the episodes does not matter, then we can use the combinatory defined as:

If we have N elements, and we want to make groups of K elements, we have

$C(N,K) = \frac{N!}{(N-K)!*K!}$

combinations.

In this case, we have a total of N = 10 episodes, and we want to make groups of  K = 2.

Then we have:

$C = (10, 2) = \frac{10!}{8!*2!} = (10*9)/(2) = 5*9 = 45$

There are 45 combinations.