Name: Linda

Who is asking: Teacher
Level: Middle

Your DJ Business has 6 rap, 10 rock, 6 alternative, 8 oldies, and 5 country CD singles. How many different 10-song sets can the DJ play, if she plays 2 singles from each category? and How many different 10-song sets if she plays exactly 3 rap singles and 4 rock singles in each set?

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  6C2 ("6 choose 2"). Similarly you can choose  10C2 rock songs,  6C2 alternative,  8C2 oldies and  5C2 country songs.

The next step is to apply the following counting principle:

If there are m ways in which to perform one action, and n ways in which to perform a second action, then there are mn ways the two actions can be performed

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,

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