[dmarsh1981]

A radio station plays three songs and four
Commercials every 20 minutes. For one 20 minute
Segment the director chooses three different songs to
Be played and the producer chooses four different
Commercials. The producer then decides that the
Order will be song, commercial, two songs, three
Commercials. How many possible arrangements are
There for this 20 minute segment?

[visharad]

Do the following steps.
1. First a song is to be played. Find out in how many ways you can select 1 song from 3 songs.

2. Then a commercial is to be played. Find out in how many ways, you can select 1 commercial from 4 commercials.

3. Then 2 songs are to be played. Initially there were three songs. One song was selected in step 1. So two remain. You will play those two songs now. Find out in how many ways these two songs can be rearranged.

4. Now 3 commercials. Find out in how many ways, these 3 commericals can be rearranged.

5. Multiply the results of steps 1 to 4. That is your answer.

Let me know if you need further help.