Question:

The number of ways in which $r$ letters can be posted in $n$ letter boxes in a town is

Updated On: Jul 15, 2023
  • $n^r$
  • $r^n$
  • $^nP_r$
  • $^nC_r$
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The Correct Option is A

Solution and Explanation

Since every letter can be posted in $n$ ways [$\because$ no of letter boxes = $n$ ] $\therefore$ total number of ways for $r$ letters $=\frac{n\times n\times......\times n}{r factors}$ $=n^{r}$
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Notes on Permutations

Concepts Used:

Permutations

A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:

\(^nP_r = \frac{n!}{(n-r)!}\)

 nPr = permutation

 n = total number of objects

 r = number of objects selected

Types of Permutation

  • Permutation of n different things where repeating is not allowed
  • Permutation of n different things where repeating is allowed
  • Permutation of similar kinds or duplicate objects