Question

In a group of 15 boys, there are 6 scouts. In how many ways can 8 boys be selected, so as to include

(i) exactly 3 scouts

(ii) at least 3 scouts

(iii) at the most 3 scouts

Answer 1

Question #15386 In a group of 15 boys, there are 6 scouts. In how many ways can 8 boys be selected, so as to include

(i) exactly 3 scouts

(ii) at least 3 scouts

(iii) at the most 3 scouts

Solution. The logic is the following choose scouts and then choose the rest boys. and then use combinatorial rule of product.

i) $\binom{6}{3}\binom{9}{5}$

ii) $\sum_{k=3}^{6} \binom{6}{k} \binom{9}{8-k}$.

iii) $\sum_{k=0}^{3} \binom{6}{k} \binom{9}{8-k}$