In a group of $6$ boys are $4$ girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there

Q. In a group of 6 batsmen and 4 bowlers, four cricketers are to be selected. In how many different ways can they be selected such that at least one batsman should be there?

Q. From a group of 7 boys and 6 girls, 5 students are to be selected to form a committee so that at least 3 boys are there on the committee. In how many ways can it be done?

Q. $1)$ A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has
$i)$ No girl$?$

$2)$ A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has
$ii)$ At least one boy and one girl$?$

$3)$ A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has
$iii)$ At least $3$ girls$?$

Q. 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?