Question
Seven children are to be seated for a group photo. Three
are cousins and should not sit together. In how many ways can this be done?Solution
7 children can be arranged among themselves in 7P7 ways = 5040 ways.
Assume that the 3 cousins are one entity. The total number of ways in which they can be arranged among themselves = 3! = 6 ways.
Also, the set of three cousins and the other students can be arranged among themselves = 5! = 120 ways.
Thus, total number of ways in which three cousins are together = 6 × 120 = 720
Thus, number of ways in which the 3 cousins will not sit together = 5040 − 720 = 4320
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