Those combinations!

Note that in the question it is mentioned that we have to select at least one boy, this means there can also be 2 or 3 or 4 of them. So at first we will consider the case of 1 boy and 3 girls, so, ways of selection are $\dbinom{6}{1}$ $\dbinom{4}{3}$ = 24. The second case comprises 2 boys and 3 girls. So, ways of selection are $\dbinom{6}{2}$ $\dbinom{4}{2}$ =90. The third case has 3 boys and 1 girl. So, ways of selection are $\dbinom{6}{3}$ $\dbinom{4}{1}$ = 80 Finally, we have 4 boys and 0 girls. So, ways of selection are $\dbinom{6}{4}$ $\dbinom{4}{0}$ = 15. So, total ways of selection are 24+90+80+15=209.