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How many ways can 5 people sit in a row if two of them insist on sitting together?
Wiki User
∙ 14y ago
(If they wouldn't want to sit together the answer would be 5! (120) but since there is a pair, we can count them as one person. So, my guess is that the answer is 4! (24))
The person who wrote this answer thought correctly that we need to consider the two person as if they are one so the answer is 4! , but still those two person can switch places between themselves so the correct answer should be 4! * 2! = 48
Wiki User
∙ 14y ago
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How many ways can 5 people sit in a row if two of them insist on not sitting together 72?
72 is correct.
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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