G Tewani Solutions for Chapter: Permutation and Combination, Exercise 1: Exercises

The number of ways of choosing a committee of two women and three men from five women and six men, if Mr.$A$ refuses to serve on the committee if Mr. $B$ is a member and Mr. $B$ can only serve, if Miss $C$ is the member of the committee is

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

The number of different ways in which five 'alike dashes' and eight 'alike dots' can be arranged using only seven of these 'dashes' and 'dots' 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

The number of integral solutions of $x+y+z=0$ with $x\ge -5, y\ge -5, z\ge -5$ is

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

The total number of ways in which $n^2$ number of identical balls can be put in $n$ numbered boxes $(1, 2, 3,\dots ,n)$ such that $i^{\text{th}}$ box contains at least $i$ number of balls is

The total number of positive integral solution of $15<x_1+x_2+x_3\le 20$ is equal to