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How many ways can 5 people sit in a row if two of them will NOT sit by each other in the row?
Wiki User
∙ 11y ago
a.b..
a..b.
a...b
.a.b.
.a..b
..a.b
6 possible ways for two people not to sit next to each other
double that to 12 if b comes before a.
there is 1x2x3 = 6 possible for the dots on each of the above 12 combinations
so answer = 6x12 = 72
* * * * *
The correct answer is derived as follows:
The total number of ways of seating 5 people in a row is 5x4x3x2x1 = 120.
Rather than work out the number of ways in which the two people do not sit together, it is simpler to work out the number of ways in which they do sit together and subtract this from the total.
For this purpose, it is possible to treat the two people as one entity and so that gives 4*3*2*1 = 24 ways. However, this number needs to be doubled to allow for the two people to swap places: making 48 such ways.
The final answer, therefore, is 120 - 48 = 72 ways.
Wiki User
∙ 11y ago
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How many ways can 5 people sit in a row if 2 of them insist on not sitting together?
The first thing to do is to work out how many ways there are without those 2 people minding. There are 5 possibilities for first place, 4 for second and so on, so the number of ways is 5x4x3x2x1 = 120. The next step is to work out how many of these possibilities have the two people sitting next to each other. There are 4 ways in which two people can sit next to each other. For each of these ways there are two possibilities, one with one person on the right, and the other with them on the left. For each of these 8 ways, there are 3x2x1=6 ways the other people could have sat. So there are 8x6=48 invalid ways in total. 120-48 = 72 So there are 72 ways 5 people can sit in a row if 2 of them insist on not sitting together.
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How many ways can 5 people sit in a row if 2 of them insist on not sitting together?
The first thing to do is to work out how many ways there are without those 2 people minding. There are 5 possibilities for first place, 4 for second and so on, so the number of ways is 5x4x3x2x1 = 120. The next step is to work out how many of these possibilities have the two people sitting next to each other. There are 4 ways in which two people can sit next to each other. For each of these ways there are two possibilities, one with one person on the right, and the other with them on the left. For each of these 8 ways, there are 3x2x1=6 ways the other people could have sat. So there are 8x6=48 invalid ways in total. 120-48 = 72 So there are 72 ways 5 people can sit in a row if 2 of them insist on not sitting together.
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