Question

In how many ways can a set of five letters be selected from the English alphabet?

Short answer

There are 65,780 ways can a set of five letters be selected from the English alphabets.

Step-by-step solution

Given data

Set of five letters

Concept of Combination

A combination is a selection of items from a set that has distinct members.

Formula:

${}_{\mathbf{n}}{\mathbf{C}}_{\mathbf{r}}\mathbf{=}\frac{\mathbf{n}\mathbf{!}}{\mathbf{r}\mathbf{!}\mathbf{(}\mathbf{n}\mathbf{-}\mathbf{r}\mathbf{)}\mathbf{!}}$

Calculation to find a set of five letters from English alphabets

A set of five letters be selected from the English alphabets are given as:

$\begin{array}{r}C(26,5)=\frac{26!}{(5!\times 21!)}\\ =65780\end{array}$

Thus, there are 65,780 ways can a set of five letters be selected from the English alphabets.