Answer to Question #201173 in Statistics and Probability for zaki

Question

From a batch containing 4 boys and 6 girls, a group of 4 students is to be selected. There are how many combinations of ⦁ 2 boys and 2 girls. ⦁ 3 boys and 1 girl. ⦁ 4 boys. ⦁ At least 2 boys Assignment expert

Answer 1

1.

$$\dbinom{4}{2}\dbinom{6}{2}=6(15)=90$$

2.

$$\dbinom{4}{3}\dbinom{6}{1}=4(6)=24$$

3.

$$\dbinom{4}{4}\dbinom{6}{0}=1(1)=1$$

4.

$$\dbinom{4}{2}\dbinom{6}{2}+\dbinom{4}{3}\dbinom{6}{1}+\dbinom{4}{4}\dbinom{6}{0}$$

$$=90+24+1=115$$