From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at leastincluding 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?

From a class of 14 boys and 10 girls, 10 students are to be chosen for a competition, at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?

From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition, including at least 4 boys.and 4 girls. The two girls who won the prizes last year should be included. In how many ways can the selection be made?

(i) In how many ways a committee of 4 members out of 5 gents and 6 ladies can be formed if there is at least one lady in the committee? (ii) From a class of 12 boys and 8 girls, 10 students are to be chosen for a competition, including at least 4 boys and 4 girls. The two boys who won the prizes last year should be included. In how many was can this selection be made?

(i) In how many ways a committee of 4 members out of 5 gents and 6 ladies can be formed if there is at least one lady in the committee? (ii) From a class of 12 boys and 8 girls, 10 students are to be chosen for a competition, including at least 4 boys and 4 girls. The two boys whho won the prizes last year should be included. In how many was can this selection be made?

From a class of 12 girls and 15 boys, 12 students are to be chosen for a competition including 7 boys and 5 girls. The two girls and 3 boys who won the prizes last year should be included . In how many ways can the selection be made ?

From a class of 12 girls and 15 boys, 12 students are to be chosen for a competition including 7 boys and 5 girls. The two girls and 3 boys who won the prizes last year should be included . In how many ways can the selection be made ?

In a class of 10 boys and 6 girls, a team of 8 has to be formed with atleast 4 boys and atleast 4 girls with the condition that two girls are always included in the team. In how many ways the selection can be made?

From 10 boys and 6 girls , how many different selections can be made so as to include at least one boy and one girl ?

Suppose one girl or one boy has to be selected for a competition from a class comprising 17 boys and 29 girls. In how many different ways can this selection be made?