Chapter 8.5, Problem 61E

To determine

To write: all possible selections of two letters that can be formed the letters.

Answer to Problem 61E

The selection can be made in 15 ways.

Explanation of Solution

Given information:

Use the letters A, B, C, D, E, and F.

Calculation:

The number of combinations of $n$ elements taken $r$ at a time is

  ${}_n{C}_r=\frac{n!}{\left(n-r\right)!r!}$

Let us consider the following letters

A, B, C, D, E, F

Choosing two letters out of 6 can be done in ${}_6{C}_2$ ways

The following are the choices of 2 letters out of 6 letters

AB

AC

AD

AE

AF

BC

BD

BE

BF

CD

CE

CF

DE

DF

EF

Therefore, total number of selection is 15.