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Schoolboy Newbie | Next Rank: 10 Posts
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Post Tue Dec 19, 2017 4:02 am
There are 3 couples sitting in a row (1 couple consists of 1 boy and 1 girl).
a. How many different sitting arrangements are possible?
b. What if one boy and one girl of a couple don't want to sit next to each other?

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elias.latour.apex Master | Next Rank: 500 Posts
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Post Fri Jan 12, 2018 5:32 am
Here's another solution that some may find easier.

We have 6 empty seats and three couples. How many people can sit in the first seat? 6 people -- any of the people waiting to be seated. However, once that happens, the person sitting next to him or her must be the other half of the couple, so we have only one choice. I will simulate this with the following notation:

(6) (1)

Once those two are seated, how many people can be seated in the third seat? 4. But once that person is seated, again, only one person can sit next to him or her. So we can notate that as:

(6) (1) (4) (1)

Finally, in the fifth seat, 2 people can be seated. So we have:

(6) (1) (4) (1) (2) (1)

And all we have to do is multiply the numbers together.

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regor60 Master | Next Rank: 500 Posts Default Avatar
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Post Thu Jan 11, 2018 1:08 pm
Schoolboy wrote:
There are 3 couples sitting in a row (1 couple consists of 1 boy and 1 girl).
a. How many different sitting arrangements are possible?
b. What if one boy and one girl of a couple don't want to sit next to each other?
a. consider each couple as a unit, So there are 3! ways to seat the 3 couples.
Within each unit there 2 ways to sit the boy and girl, so need to multiply 3! by 2^3 equaling 48 ways to sit the 3 couples

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Post Sun Dec 24, 2017 7:09 am
Well, the answer to your first question is fairly easy. We have three couples that can go in three locations:

C1, C2, C3

How many ways can they be organized? Well, initially we would need to select one couple to go far left. We have three choices. Then we would select the couple to go in the middle. We have two choices for that. Then the last couple would go in the far right location. So we would have 3x2x1 or 3! possibilities.

But that is not all. We must consider how the couples are arranged. We might have the man on the right and the woman on the left, or vice versa. So the number of possibilities are double.

From that number, we would need to calculate the number of ways that one boy and one girl might sit together and subtract those possibilities. They are:

xbgxxx
xgbxxx
xxxbgx
xxxgbx

So four.

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Elias Latour
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