Here are my problems:(adsbygoogle = window.adsbygoogle || []).push({});

1) Suppose seven school children (3 girls and 4 boys) are lined up to board a school bus. Find the number of ways they could line up if no two boys are together.

This arrangement would be BGBGBGB. So if I consider each BG as a unit, then there are 4! arrangements. But within the BG groupings, the B and G can switch places. So shouldn't the number of ways be 4!2!2!2! Is this correct?

2) Among ten lottery finalists, four will be selected to win individual amounts of $1000, 2000, 5000, and 10000. In how many ways can the money be distributed?

I know that 10 choose 4 is 210. But don't I have to do something else? A permutation perhaps?

Thanks for the help in advance!

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# Counting Problems

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