Question

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

Answer 1

5 boys can be selected from 25 boys in 25C5 ways

3 girls can be selected from 10 in 10C3 ways

noof boat parties = 25C5×10C3

=(25×24×23×22×21)/(1×2×3×4×5)×10×9×8/(1×2×3)

=53830×120

=6459600

Answer 2

6375600 no. of different boat parties of 8, consisting of 5 boys and 3 girls, can be made

Step-by-step explanation:

Total no. of boys = 25

Total no. of girls = 10

We are supposed to form a group of 5 boys and 3 girls

So, Out of 25 , 5 boys will be chosen

Our of 10 girls, 3 girls will be chosen

So, No. of different boat parties = $^{25}C_5 \times ^{10}C_3$

Formula :$^nC_r=\frac{n!}{r!(n-r)!}$

So,  No. of different boat parties =$\frac{25!}{5!(25-5)!} \times \frac{10!}{3!(10-3)!}=6375600$

Hence 6375600 no. of different boat parties of 8, consisting of 5 boys and 3 girls, can be made

#Learn more :

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