D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Permutations & Combinations, Exercise 2: Exercise 2

In how many ways can a committee of $5$ made out $6$ men and $4$ women containing atleast one woman?

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

How many integers greater than $5000$ can be formed with the digit $7, 6, 5, 4$ and $3,$ using each digit at most once

Rajdhani express going from Bombay to Delhi stops at $5$ intermediate stations. $10$ passengers enter the train during the journey with ten different tickets of two classes. The number of different sets of tickets they may have is

The total number of permutation of $n\mathit{ }\left(\mathit{n}\mathit{>}\mathit{1}\right)$ different things taken not more than $r$ at a time, when each thing may be repeated any number of times, is

If the letters of the word $KRISNA$ are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word $KRISNA$ is

The number of ways in which $20$ different pearls of two colours can be set alternately on a necklace, there being $10$ pearls of each colour, is 

Let $A=\left\{x\right|x$ is a prime number and $x<30\}$. The number of different rational numbers whose numerator and denominator belong to $A$ is