Question

A group consists of $4$ girls $\&7$ boys, In how many ways can a team of $5$ members be selected if the team has "at least one boy $\&$ one girl?

Answer 1

At least one boy and one girl

Girls (out of $4$) Boys (out of $7$) Number of ways

$1$ $4$ ${}^4{C}_1{\times }^7{C}_4=140$

$2$ $3$ ${}^4{C}_2{\times }^7{C}_3=210$

$3$ $2$ ${}^4{C}_3{\times }^7{C}_2=84$

$4$ $1$ ${}^4{C}_4{\times }^7{C}_1=07$

$\therefore$ Required number of ways

$=140+210+84+07=441$