D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Permutations & Combinations, Exercise 1: Exercise 1

With $17$ consonants and $5$ vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is

In a class of $10$ students, there are $3$ girls. In how many different ways can all the students be arranged in a row such that no two of the three girls are consecutive

The number of words that can be formed out of the letters of the word $\mathrm{COMMITTEE}$ is

In how many ways can $5$ prizes be distributed among $4$ boys when every boy can take one or more prizes?

If ${}^{10}P_r=720,$ then $r$ is equal to

The number of ways in which $n$ distinct objects can be put into two different boxes so that no box remains empty is

The number of ways of selecting exactly $4$ fruits out of $4$ apples, $5$ mangoes and $6$ oranges is 

Three dice are rolled. The number of possible outcomes in which at least one die shows $5$ is