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Question
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
Solution
Clearly, out of the 25 boys and 10 girls, 5 boys and 3 girls will be chosen.
Then, different boat parties of 8 =\[{}^{25} C_5 \times^{10} C_3\]
\[ = \frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} \times \frac{10 \times 9 \times 8}{3 \times 2 \times 1}\]
\[ = 6375600\]
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