Embibe Experts Solutions for Chapter: Permutation & Combination, Exercise 2: Exercise

Fifteen identical balls have to be put in five different boxes. Each box can contain any number of balls. The total number of ways of putting the balls into the boxes so that each box contains at least two balls is equal to

Let $f(n,k)$ denote the number of ways in which $k$ identical balls can be coloured with $n$ colours so that there is at least one ball of each colour. Then $f(2n,n)$ must be equal to

In a polygon, no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon is $70,$ then the number of diagonals of the polygon is

$A$ is a set containing $\text{'}n\text{'}$ different elements. A subset $P$ of $A$ is chosen. The set $A$ is reconstructed by replacing the elements of $P.$ A subset $Q$ of $A$ is again chosen. The number of ways of choosing $P$ and $Q$ so that  $P\cap Q$ contains exactly two elements is

$20$ persons are sitting in a particular arrangement around a circular table. Three persons are to be selected for leaders. The number of ways of selection of three persons such that no two were sitting adjacent to each other is

$n$ is selected from the set $\{1, 2, 3, \dots \dots ., 100\}$ and the number $2^n+3^n+5^n$ is formed. Total number of ways of selecting $n$ so that the formed number is divisible by $4$ is equal to

In a certain test, there are $n$ questions. In the test $2^{n-1}$ students gave wrong answers to at least $i$ questions, where $i=1, 2, \dots .. n.$ If the total number of wrong answers given is $2047,$ then $n$ is equal to

Rajdhani Express going from Bombay to Delhi stops at five intermediate stations, $10$ passengers enter the train during the journey with $10$ different ticket of two classes. The number of different sets of tickets they may have is