Question

The number of possible ways for r letters to be delivered to n letter boxes in a town is:

Answer 1

Hint: We will first see the definition of combination and try to understand its formula. It is very important to understand each question very clearly because we will have some variation. We will also see the formula of combination.

Complete step-by-step answer:
Permutation and combination are methods for representing a collection of things by picking them from a set and dividing them into subsets. It specifies the numerous methods for organizing a set of data.
We know that a combination is a mathematical process that determines the number of alternative arrangements in a collection of objects in which the items are chosen in any order.
The combination formula is \[^n{C_r} = \dfrac{{n!}}{{\left( {n - r} \right)!\:\:r!\:}}\]
where n is the total number of items in the set and r denotes the number of items used in the permutation to determine n's value.
Any of the letter boxes can be used to post the letters. This means that each letter can be delivered to multiple letter boxes. If \[n\] letters can be posted in \[m\] letter boxes, then the number of ways of posting \[n\] letters in \[m\] boxes is \[{m^n}\]
Hence, the number of ways r letters can be delivered to n letter boxes is ${n^r}$${n^r}{m^n}$

Note: A permutation is any of the various arrangements that can be constructed by taking some or all of a number of elements. The number of permutations of m separate objects taken n at a time that can be repeated is \[{m^n}\].