# How many four letter words are possible using the first 5 letters of the alphabet if the first letter can not be a and adjacent letters can not be alike?

Jan 26, 2016

The first five letters are $A , B , C , D , E$

Consider this box.

Each $1 , 2 , 3 , 4$ places represent place of a letter.

First place $1$ can be filled in $4$ ways. (Excluding A)
First place $2$ can be filled in $4$ ways.
First place $1$ can be filled in $3$ ways.
First place $1$ can be filled in $2$ ways.
First place $1$ can be filled in $1$ ways.

Total number of ways$= 4 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 96 w a y s$

Hence $96$ letters can be made.