Amit M Agarwal Solutions for Chapter: Permutation and Combination, Exercise 7: Target Exercises

$n$ different toys have to be distributed among $n$ children. The total number of ways in which these toys can be distributed, so that exactly one child gets no toy, is equal to

The total number of permutations of $k$ different things, in a row, taken not more than $r$ at a time (each thing may be repeated any number of times) is equal to

The total number of numbers that are less than $3·{10}^8$ and can be formed using the digits $1, 2, 3,$ is equal to

Four couples (husband and wife) decide to form a committee of four members. The number of different committees that can be formed in which no couple finds a place, is

In an examination of $9$ papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful, is

The number of $5$-digit numbers that can be made using the digits $1$ and $2$ and in which at least one digit is different, is

In a club election, the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote be $62$, then the number of candidates is

Two players $P_1$ and $P_2$ play a series of $2n$ games. Each game can result in either a win or loss for $P_1$. Total number of ways in $P_1$ which can win the series of these games, is equal to