R S Aggarwal Solutions for Exercise 2: EXERCISE 9B

Find the number of ways of selecting $9$ balls from $6$ red balls, $5$ white balls and $4$ blue balls if each selection consists of $3$ balls of each colour.

How many different boat parties of $8$ consisting of $5$ boys and $3$ girls can be made from $20$ boys and $10$ girls?

In how many ways can a student choose $5$ courses out of $9$ courses if $2$ specific courses are compulsory for every student?

A sports team of $11$ students is to be constituted, choosing at least $5$ from class $\mathrm{XI}$ and at least $5$ from class $\mathrm{XII}$. If there are $20$ students in each of these classes, in how many ways can the team be constituted?

From $4$ officers and $8$ clerks, in how many ways can $6$ be chosen to include exactly one officer?

From $4$ officers and $8$ clerks, in how many ways can $6$ be chosen to include at least one officer?

A cricket team of $11$ players is to be selected from $16$ players including $5$ bowlers and $2$ wicketkeepers. In how many ways can a team be selected so as to consist of exactly $3$ bowlers and $1$ wicketkeeper?

A committee of three 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?