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How many different arrangements of letters are possible

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by M7MBA » Sun Feb 18, 2018 4:35 am
How many different arrangements of letters are possible, if three letters are chosen without replacement from the letters A, B, C, D, and E to make the arrangement?

A. 120
B. 60
C. 20
D. 10
E. 6

The OA is the option B.

I don't understand the question. Can any expert give me some help here? Thanks in advanced.
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by [email protected] » Sun Feb 18, 2018 10:55 am
Hi M7MBA,

We're asked for the number of different arrangements of three letters are possible if the letters A, B, C, D, and E are chosen - WITHOUT replacement - to make the arrangement. This is a standard permutation question and requires just a little arithmetic to solve.

Since we're NOT allowed to 'reuse' a letter, each letter chosen reduces the options for the letter that can be chosen next:
5 options for the 1st letter
4 options for the 2nd letter
3 options for the 3rd letter

(5)(4)(3) = 60 total arrangements of 3 letters.

Final Answer: B

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by Jeff@TargetTestPrep » Wed Feb 21, 2018 1:38 pm
M7MBA wrote:How many different arrangements of letters are possible, if three letters are chosen without replacement from the letters A, B, C, D, and E to make the arrangement?

A. 120
B. 60
C. 20
D. 10
E. 6
The number of ways to arrange 3 letters from 5 (where order matters) is 5P3 = 5!/2! = 5 x 4 x 3 = 60.

Answer: B

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