Sarvesh K Verma Solutions for Chapter: Permutations & Combinations, Exercise 3: Introductory Exercise

How many numbers of $5$digits can be formed with the digits $0,2,3,4$ and $5$ if the digits may repeat?

How many numbers each lying between$9$and $1000$ can be formed with the digits $0,1,2,3,7,8$(numbers can be repeated)?

Number of natural numbers not exceeding $4321$ can be formed with the digits $1,2,3,4$ if repetition is allowed is

In how many ways can $5$ prizes be given away to $4$ boys when each boy is eligible for any number of prizes? 

In how many ways can $\text{n}$balls be randomly distributed in $\text{n}$ cells?