From 10 names on a ballot, a committee of 3 will be elected to attend a political national 11) convention. How many different committees are possible?



Answer to a math question From 10 names on a ballot, a committee of 3 will be elected to attend a political national 11) convention. How many different committees are possible?

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1. Calculate the number of ways to choose 3 names from 10 (combination formula):
\binom{10}{3} = \frac{10!}{3!(10-3)!}
2. Simplify the factorials:
\binom{10}{3} = \frac{10!}{3! \cdot 7!}
3. Cancel out the common terms in the factorials:
\binom{10}{3} = \frac{10 \cdot 9 \cdot 8}{3 \cdot 2 \cdot 1} = 120
4. Final answer:
\binom{10}{3} = 120

Therefore, the number of different committees possible is 120 .

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