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Ryan Ziemba
- Junior | Next Rank: 30 Posts
- Posts: 25
- Joined: Thu May 27, 2010 8:34 pm
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Here's the question I've been trying to get a handle on:
In how many different ways can the letters A, A, B, B, B, C, D, E be arranged if the letter C must be to the right of the letter D?
A. 1,680
B. 2,160
C. 2,520
D. 3,240
E. 3,360
I understand what I considered the first step of the problem where we would have to de-duplicate the repeating terms by division.
So 8!/(2!)(3!) or 8*7*6*5*4*3*2*1 / (2*1)*(3*2*1)
I become lost, however, when attempting to apply the restriction limiting C's placement to the right of the letter D.
The resource from which I took this problem suggests approaching the restrictive element by dividing again by two, so 8!/(2!)(3!)(2).
The premise for this, the explanation goes on, is that "For any specified locations of the letter C and the letter D, there are the same number of arrangements for the other 6 letters when C is to the right of D and D is to the right of C. So we must divide the number of possible arrangements of all the letters by 2."
This is the part I don't quite understand and I would really appreciate any insight into how to resolve the part of the problem involving the restriction on the order of C & D as well as any other restriction related pearls of wisdom you may willing to impart.
In how many different ways can the letters A, A, B, B, B, C, D, E be arranged if the letter C must be to the right of the letter D?
A. 1,680
B. 2,160
C. 2,520
D. 3,240
E. 3,360
I understand what I considered the first step of the problem where we would have to de-duplicate the repeating terms by division.
So 8!/(2!)(3!) or 8*7*6*5*4*3*2*1 / (2*1)*(3*2*1)
I become lost, however, when attempting to apply the restriction limiting C's placement to the right of the letter D.
The resource from which I took this problem suggests approaching the restrictive element by dividing again by two, so 8!/(2!)(3!)(2).
The premise for this, the explanation goes on, is that "For any specified locations of the letter C and the letter D, there are the same number of arrangements for the other 6 letters when C is to the right of D and D is to the right of C. So we must divide the number of possible arrangements of all the letters by 2."
This is the part I don't quite understand and I would really appreciate any insight into how to resolve the part of the problem involving the restriction on the order of C & D as well as any other restriction related pearls of wisdom you may willing to impart.
