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?

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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?

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Answer 1 · 2016-01-26T12:34:18

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

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Consider this box.

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

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

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

Hence $96$ $96$ letters can be made.

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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?

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