Suppose that there are 14 songs on a cd and you like 8 of them. When using the random button selector on a cd player, each of the 14 songs is played once in a random order. Find the probability that among the first 3 songs that are played, you like exactly two of them.
So what I've done so far is to calculate the number of ways to like 2 songs
8 C 2
I then multiply this by the dislike of the third song
6 C 1
and then I divide by the number of ways to play 3 songs out of 14 total
14 C 3
So I have (8 C 2) * (6*1) / (14 C 3)
Is this correct?