# How many different boat parties of 8, consisting of 5 boys and 3 girls,

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 $8={ }^{25} C_{5} \times{ }^{10} C_{3}$

$=\frac{25 !}{5 ! 20 !} \times \frac{10 !}{3 ! 7 !}$

$=\frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} \times \frac{10 \times 9 \times 8}{3 \times 2 \times 1}$

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