Khizra K. 1 Expert Answer Your question is not entirely clear to me. If they insist in being lined up in a specific order there are, in effect, only four objects to be arranged: three individuals and this group, so that would be 4! possible arrangements. 4! = 24 different ways. If they merely insist on being together, but do not care how they are lined up so long as they are together, you would still have four objects 4!, but one of those objects could be in 3! different states. 4!3! = (24)(6) = 144 different ways.
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There are ways that 6 people can be lined up to get on the bus. (That is because there are 6 ways to choose who is first, for each of those choices, there are 5 ways to choose who is second, and so on).There are ways to line up 6 people placing together the 2 people who refuse to be next to each other.{That is because there are ways to arrange the other 4 people, ways to arrange the 2 people who refuse to be next to each other, and places to insert the problem pair in the line formed by tho other 4). Since of the ways that 6 people can be lined up to get on the bus place together the 2 people refuse to be next to each other,there are ways to line up the 6 people keeping apart the 2 people who refuse to be next to each other. |