R D Sharma Solutions for Chapter: Combinations, Exercise 4: VERY SHORT ANSWER QUESTIONS (VSAQs)

Write $\sum _{r=0}^m{}^{n+r}C_r$ in the simplified form.

If the value of $\sum _{r=1}^6{}^{56-r}C_3+{}^{50}C_4={}^{x}C_y$ then find the value of $\left(x+y\right)$.

There are $3$ letters and $3$ directed envelopes. Write the number of ways in which no letter is put in the correct envelope.

Write the maximum number of points of intersection of $8$ straight lines in a plane.

Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.

Write the number of ways in which $5$red and $4$ white balls can be drawn from a bag containing $10$red and $8$ white balls.

The number of ways in which $12$ boys may be divided into three groups of $4$ boys each are $\frac{a!}{(4!{)}^3\times b!}$, then find the value of $\left(a+b\right)$.

Write the total number of words formed by $2$vowels and $3$ consonants taken from $4$ vowels and $5$ consonants.