R S Aggarwal Solutions for Exercise 6: EXERCISE 5F

How many $7-$digit numbers can be formed using the digits $1, 2, 0, 2, 4, 2$ and $4$?

How many numbers can be formed with the digits $1, 2, 3, 4, 3, 2, 1$ so that the odd digits always occupy the odd places?

How many different signals can be made from $4$ red, $2$ white and $3$ green flags by arranging all of them vertically on a flagstaff?

How many $3-$digit numbers can be formed by using the digits $0, 1, 3, 5, 7$ while each digit may be repeated any number of times?

In how many ways can $4$ letters be posted in $3$ letter boxes?

In how many ways can $5$ prizes be distributed among $4$ students, when each student may receive any number of prizes? [Write your answer in four digits]

How many natural numbers less than $1000$ can be formed from the digits $0, 1, 2, 3, 4, 5$ when a digit may be repeated any number of times?

A boy has $6$ pockets. In how many ways can he put $5$ marbles in his pocket?  [Write your answer in four digits]