How many ways can the letters A, B, C and D be arranged if the first letter should be a consonant with repetitions?

Expert Answers

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There are four letters given. These are A, B, C and D.

And there are four positions that have to be filled up.

___    ___    ___    ___ 

 

The first position must be filled up with consonant only, which are B, C and D. So there are only three consonants that we can pick from for the first position.

`ul3`     ___    ___    ___ 

Since repetition is allowed, the second position can be filled by A, B, C or D. So there are four possible letters than can occupy the second position.

`ul3`    `ul4`     ___    ___     

Also, the third and fourth position, can be filled by A, B, C or D. So there are four possible letters that can be place in the third and fourth position.

`ul3`    `ul4`    `ul4`    `ul4`

And, multiply them together.

`ul3 * ul4 * ul4 * ul4 = 192`

 

Therefore, if the first letter should be a constant and repetition is allowed, there 192 ways that A, B, C and D can be arranged.

Approved by eNotes Editorial Team

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