SOLUTION: A committee of 3 people is to be selected from a group of 10 people so that there is one president, one treasurer, and one senator. In how many ways is this done?

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Question 532645: A committee of 3 people is to be selected from a group of 10 people so that there is one president, one treasurer, and one senator. In how many ways is this done?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A committee of 3 people is to be selected from a group of 10 people so that there is one president, one treasurer, and one senator. In how many ways is this done?
You can choose the president any of 10 ways.

For each of those 10 choices, there will remain 9 choices for picking the
treasurer.  That's 10×9 (or 90) ways to pick the president and
treasurer.

For each of those 10×9 or 90 ways to pick the president and treasurer, there
remain 8 ways to pick the senator.  So that's 10×9×8 or 90×8 or 720 ways to
fill all three offices.

Edwin