Chapter 9.6, Problem 57E

To determine

Find all combinations of two letters formed from the A, B, C, D, E and F.

Answer to Problem 57E

The combinations are

AB, AC, AD, AE, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF

Explanation of Solution

Given:

Six letters: A, B, C, D, E, F

Choose any two letters from the 6 letters A, B, C, D, E, F

It can be done in NA ways

  ${}_6{C}_2=\frac{6!}{2!(6-2)!}\left({}_m{C}_r=\frac{n!}{r!(n-r)!}\right)$

  $\begin{array}{l}=\frac{6\cdot 5\cdot 4!}{2\cdot 4!}\hfill \\ =3\cdot 5\hfill \\ =15\hfill \end{array}$

Hence the combination of two letters that can be formed with A,B,C,D,E,F is 15.

Those combinations are

AB, AC, AD, AE,BC ,BD, BE, BF, CD, CE, CF, DE, DF,EF