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| − | 2.2b: In how many ways can 8 people be seated in a row if persons A and B must sit next to each other? | + | '''2.2b: In how many ways can 8 people be seated in a row if persons A and B must sit next to each other?''' |
Consider persons A and B to act like "one person" -- i.e., they cannot be divided. Therefore, that leaves us with two questions: In how many ways can we arrange 7 people/groups, and in how many ways can we arrange A and B? (For each arrangement of 7 people/groups, each group within can sit in a certain number of ways.) | Consider persons A and B to act like "one person" -- i.e., they cannot be divided. Therefore, that leaves us with two questions: In how many ways can we arrange 7 people/groups, and in how many ways can we arrange A and B? (For each arrangement of 7 people/groups, each group within can sit in a certain number of ways.) | ||
Latest revision as of 11:27, 9 September 2008
2.2b: In how many ways can 8 people be seated in a row if persons A and B must sit next to each other?
Consider persons A and B to act like "one person" -- i.e., they cannot be divided. Therefore, that leaves us with two questions: In how many ways can we arrange 7 people/groups, and in how many ways can we arrange A and B? (For each arrangement of 7 people/groups, each group within can sit in a certain number of ways.)
The 7 people/groups can sit in 7*6*5*...*1 = 7! ways. For each way the 7 people/groups sit, A and B (one of these "people") can sit in 2*1 = 2! ways.
Thus, there are 7!2! ways that the people can sit.
