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counting and probability intermediate

Problem

The Grammar club has 20 members: 10 boys and 10 girls. A 4-person committee is chosen at random. What is the probability that the committee has at least 1 boy and at least 1 girl?
Solution
The number of ways to choose a committee of all boys or all girls is . The total number of committees is . Thus the answer is .
Final answer
\dfrac{295}{323}