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How Many Different Boat Parties of 8, Consisting of 5 Boys and 3 Girls, Can Be Made from 25 Boys and 10 Girls? - Mathematics

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How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?

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Solution

Clearly, out of the 25 boys and 10 girls, 5 boys and 3 girls will be chosen.

Then, different boat parties of 8 =\[{}^{25} C_5 \times^{10} C_3\] 

\[= \frac{25!}{5! 20!} \times \frac{10!}{3! 7!}\]
\[ = \frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} \times \frac{10 \times 9 \times 8}{3 \times 2 \times 1}\]
\[ = 6375600\]
Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 2 | Page 15

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