M L Aggarwal Solutions for Chapter: Permutations and Combinations, Exercise 3: EXERCISE 8.3

How many odd numbers greater than $80000$ can be formed using the digits $2,3,4,5$ and $8$ if each digit is used only once in a number?

How many numbers greater than $20000$ can be formed by using the digits $0, 1, 2, 3, 4$ with no digit being repeated?

A moped license plate has two letters and then four numbers in it. How many plates can be made without duplicating, there are no plates with number zero? What is the use of High Security Registration Plate? 

In an examination, there are three multiple choice questions and each question has four choices. Find the number of ways in which a student can fail to get all correct answers.

There are three prizes to be distributed among $6$ boys. In how many ways can it be done when no boy gets more than one prize.

There are three prizes to be distributed among $6$ boys. In how many ways can it be done when there is no restriction as to the number of prizes any boy gets.

There are three prizes to be distributed among $6$ boys. In how many ways can it be done when no boy gets all the prizes?

There are $3$ candidates and $5$ voters. In how many ways can the votes be given? If $3$ candidates are among $5$ voters and they vote for themselves only, then how many ways of giving votes are possible? Why should everyone vote?