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?

(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?

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 32 students, 4 are to be chosen for a competition. In how many ways can this be done?

From a class of 30 student , 3 are to be chosen for a competition . In how many ways can this be done ?

Five boys and five girls sit alternately around a round table. In how many ways can this be done?

Five boy and five girls sit alternately around a round table. In how many ways can this be done?

From a class of 15 students, 10 are to be chosen. There are 3 students who decide that either all of them will select or non of them will select. In how many ways can they be chosen?

In a class, there are 15 boys and 10 girls. How many ways a teacher can select 1 boy and 1 girl to represent the class at a seminar.

There are 12 boys and 8 girls in a class (i) In how many ways can a boy be selected? (ii) In how many ways can one boy and one girl be selected?

In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?