R D Sharma Solutions for Chapter: Combinations, Exercise 2: EXERCISE 17.2

In how many ways can one select a cricket team of eleven from $17$ players in which only $5$ persons can bowl if each cricket team of $11$ must include exactly $4$ bowlers?

A bag contains $5$ black and $6$ red balls. Determine the number of ways in which $2$ black and $3$ red balls can be selected.

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

A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
exactly $3$ girls?

A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
at least $3$ girls?

A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
at most $3$ girls?

In an examination, a question paper consists of $12$ questions divided into two parts i.e., Part $\mathrm{I}$ and Part $\mathrm{I}\mathrm{I}$, containing $5$ and $7$ questions, respectively. A student is required to attempt $8$ questions in all, selecting at least $3$ from each part. In how many ways can a student select the questions?

A parallelogram is cut by two sets of $m$ lines parallel to its sides. Find the value of $k$ if the number of parallelograms thus formed is ${}^{k}C_2\times {}^{k}C_2$.