Amit M Agarwal Solutions for Chapter: Permutation and Combination, Exercise 4: Work Book Exercise 6.4

The number of ways in which a mixed double game can be arranged from amongst $9$ married couples, if no husband and wife play in the same game, is

The number of different seven digit-numbers that can be written using only the three digits $1,2$ and $3$ with the condition that the digit $2$ occurs twice in each number, is

The number of ways one can put $5$ different balls in $5$ different boxes such that at most three boxes are empty, is

Given that $n$ is odd, the number of ways in which three numbers in $AP$ can be selected from $1,2,3,\dots ,n,$ is

The number of ways in which we can sẹlect four numbers from $1$ to $30,$ so as to exclude every selection of four consecutive numbers, is

The number of ways in which $10$ candidates $A_1,A_2,\dots ,A_{10}$ can be ranked, so that $A_1$ is always above $A_2$, is

There are $n$ white and $n$ black balls marked $1,2,3,\dots , n$. The number of ways in which we can arrange these balls in a row, so that neighbouring balls are of different colours, is

A man invites a party to $\left( m+n\right)$ friends to dinner and places $m$ at one round table and $n$ at another. The number of ways of arranging the guests is