Probability Question

Question

A radio disc jockey has 7 songs on this upcoming hour's playlist: 3 are rock songs, 2 are reggae songs, and 2 are country songs. The disc jockey randomly chooses the first song to play, and then she randomly chooses the second song from the remaining ones. What is the probability that the first song is a country song and the second is a reggae song? Write your answer as a fraction in simplest form.

Answer 1

There are two ways to solve this.  Solving as Kenneth did, the denominator should be permutations (combinations or permutations in the numerator don't matter, as we are only choosing one, but to be consistent, we have permutations here as well).

2P1*2P1/7P2 = 2*2/(7*6) = 4/42 = 2/21

Using conditional probability, the chance of the first song being country is 2/7.  Then, there are only 6 songs left, 2 of which are reggae, so the probability of picking a reggae song is 2/6.  2/7 * 2/6 = 4/42 = 2/21

Answer 2

this computation is 2C1•2C1÷7C2 based on two choices for the first (country) song, 2 choices for the second (reggae) out of all possible combinations of any two songs chosen from the total of 7 that were available.