Name: Linda
Who is asking: Teacher
Question: Hi Linda, For this question I would take it in steps. For example, if the DJ needs to play 2 rap songs and there are six to choose from, how many ways are there to choose 2 from the 6. The answer is _{6}C_{2} ("6 choose 2"). Similarly you can choose _{10}C_{2} rock songs, _{6}C_{2} alternative, _{8}C_{2} oldies and _{5}C_{2} country songs. The next step is to apply the following counting principle: By generalizing this rule for the case when there are more than just 2 actions (as in this case where there are five), we find that multiplying the indivudual results from step 1 together will yield the answer you are looking for.
Hope this helps,
