For the post of 5 teachers, there are 23 applicants, 2 posts are reserved for SC/ST candidates and there are 7 SC/ST candidates among the applicants. In how many ways can the selection be made?

We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made ?

In an Examination, a candidate has to pass in each of the four subjects. In how many ways can he fail ?

There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. In how many ways can the votes be given ?

A committee of 2 boys is to be selected from 4 boys. In how many ways can this be done ?

In how many ways can 5 sportsmen be selected from a group of 10 ?

At an election, a voter may vote for any number of candidates not greater than the number to be chosen. There are 7 candidates and 4 members are to be chosen. In how many ways can a person vote ?

From a class of 12 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 ?

A family consists of a grandfather, 5 sons and daughters and 8 grand child. They are to be seated in a row for dinner. The grand children wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. In how many ways can the family be made to sit?

In a class there are 30 boys and 18 girls. The teacher wants to select one boy and one girl to represent the class for a quiz competition. In how many ways can the teacher make this selection ?

In a village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme, 20 families are to be chosen for assistance, of which at least 18 families must have atmost 2 children. In how many ways can the choice be made ?