I was just helping a student with his AoPS homework, when I came across the following related problems:

Eight people, including Fred, are in a club. They decide to form a 3 person committee. How many possible committees can be formed?

So we are choosing 3 people out of 8 or .

How many possible committees include Fred?

Since Fred is taking one committee seat, that means we need to choose 2 more people from the remaining seven, or .

How many possible committees do not include Fred?

Since we can’t choose Fred, we need to choose 3 members from the remaining 7 or .

Since the total number of committees is equal to the number of of committees with Fred plus the number of committees without Fred, then we can say

.

Generally we call this Pascal’s Rule: .

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## Published by mathproblemsolvingskills

I coach students preparing for MathCounts and the AMCs, and I teach using curricula published by Art of Problem Solving.
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