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 ?

A committee consisting of 2 men and 2 women is to be chosen from 5 men and 6 women. IN how many ways can this be done?

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 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

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?

Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?