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Question:** A chemist at Caltech is testing combinations of 4 different catalysts for a reaction from a set of 9 available catalysts. How many distinct sets of 4 catalysts can be selected?
Solution:** This is a combinations problem where we need to choose 4 catalysts from 9. The number of ways to do this is given by:
\binom{9}{4} = \frac{9!}{4!(9-4)!} = \frac{9 \times 8 \times 7 \times 6 \times 5!}{4! \times 5!} = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}

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