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?

1 Answer
Jan 26, 2016

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

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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*4*3*2*1=96 ways#

Hence #96# letters can be made.