R S Aggarwal Solutions for Exercise 4: EXERCISE 9D

If ${}^{35}C_{n+7}={}^{35}C_{4n-2}$ then find the value of $n$.

The number of diagonals in an $n-$sided polygon is $\frac{n\left(n-k\right)}{2}$. Find $k$

Three persons enter a railway compartment having $5$ vacant seats. In how many ways can they seat themselves?

There are $12$ points in a plane, out of which $3$ points are collinear. How many straight lines can be drawn by joining any two of them?

In how many ways can committee of $5$ be made out of $6$ men and $4$ women, containing at least $2$ women?

There are $13$ cricket players, out of which $4$ are bowlers. In how many ways can team of $11$ be selected from them so as to include at least $3$ bowlers?

How many different committees of $5$ can be formed from $6$ men and $4$ women, if each committee consists of $3$ men and $2$ women?

How many parallelograms can be formed from a set of $4$ parallel lines intersecting another set of $3$ parallel lines?