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Bunuel
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How many different arrangements of the letters A, B, C, D, and E are 26 Dec 2016, 11:05
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

Question Stats:

93% (00:42) correct 7% (01:36) wrong based on 123 sessions

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How many different arrangements of the letters A, B, C, D, and E are possible where A occupies the middle position and all letters must be used?

A. 60
B. 48
C. 24
D. 12
E. 6
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C
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How many different arrangements of the letters A, B, C, D, and E are 26 Dec 2016, 21:15
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4[u] 3 a 2 1[/u]
24
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How many different arrangements of the letters A, B, C, D, and E are 27 Dec 2016, 09:08
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Bunuel
How many different arrangements of the letters A, B, C, D, and E are possible where A occupies the middle position and all letters must be used?

A. 60
B. 48
C. 24
D. 12
E. 6
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__ __ A __ __

The first place can be filled by B,C,D or E - In 4 ways
The Second place can be filled by B,C,D or E - In 3 ways
The Fourth place can be filled by B,C,D or E - In 2 ways
The Fifth place can be filled by B,C,D or E - In 1 way

So, The total No of ways will be 4*3*2*1 = 24 ways...

Correct answer will definitely be (C) 24
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How many different arrangements of the letters A, B, C, D, and E are 27 Dec 2016, 09:38
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Let us use the counting spaces method to solve this question.

2 key things to note here.
    1. The third place is filled by the letter "A", so we have only 4 places left to fill
    2. There are no constraints on the letters that can occupy these 4 places. Hence, we can use any letter to fill any place.


The first place can be filled in 4 ways. We can chose any one of the four lettters - B, C, D or E.
On doing so we are left with only 3 choices for the second place. Similarly, on filling the second place, we will be left with only 2 choices to fill the fourth place and only one way to fill the last place.

Hence, the total number of arrangements = \(4*3*2*1=24\). Correct answer is Choice C.
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