R S Aggarwal Solutions for Exercise 1: EXERCISE

$12$ persons meet in a room and each shakes hands with all the others. How many handshakes are there?

In how many ways can we select $9$ balls out of $6$ red balls, $5$ white balls and $5$ blue balls if $3$ balls of each colour are selected?

In how many ways can a cricket team be chosen out of a batch of $15$ players, if a particular player is always chosen?

In how many ways can a cricket team be chosen out of a batch of $15$ players, if a particular player is never chosen?

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

In how many ways can $5$ white balls and $3$ black balls be arranged in a row so that no two black balls are together?

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

An examination paper contains $12$ questions consisting of two parts, $A$ and $B$. Part $A$ contains $7$ questions and part $B$ contains $5$ questions. $A$ candidate is required to attempt $8$ questions, selecting at least $3$ from each part. In how many ways can the candidate select the questions?