Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: Exercise 1

Let $N$ denote the number of ways in which $n$ boys can be arranged in a line so that $3$ particular boys are separated then, then $N$ is equal to

If the sum of all numbers greater than $10000$ formed by using the digits $0,1,2,4,5$ & no digit being repeated in any number, is $N$, then sum of digits of $N$ is

There are $5$ balls of different colours & $5$ boxes of colours same as those of the balls. The number of ways in which the balls, one in each box could be placed such that exactly one ball goes to the box of its own colour are

Let $15$ identical candy bars be distributed between Ram, Shyam, Ghanshyam and Balram, if Ram can not have more than $5$ candy bars and Shyam must have at least two are $N$, then sum of digits of $N$ is (Assume all candy bars to be alike)

A shop sells $6$ different flavours of ice-creams. Let the number ways can a customer choose $4$ ice-cream cones

(a) are $M$, if they are all different flavours.

(b) are $N$, if they are not necessarily of different flavours.

(c) are $P$, if they contain only $3$ different flavours.

(d) are $Q$, if they contain only $2$ or $3$ different flavours.

Find the value of $\left(N+P\right)-\left(M+Q\right)$.

Number of octagons that can be formed by using vertices of $20$ sided polygon such that no side of octagon is common with side of polygon is given by ${}^{13}C_{r_1}-{}^{11}C_{r_2}$ then minimum value of $r_1+r_2$ is equal to___

If number of ways in which a selection of $100$ balls, can be made out of $100$ identical red balls, $100$ identical blue balls & $100$ identical white balls is $N$, then sum of digits of $N$ is

Let $S\left(n\right)$ denote the number of ordered pairs $\left(x,y\right)$ satisfying $\frac{1}{x}+\frac{1}{y}=\frac{1}{n}$ where $n>1$ and $x,y\in N$ then value of $S\left(6\right)$ is equal to____