Question
Six students are to be seated in a row. Four of them are
boys and the rest are girls. In how many ways can they be arranged such that the two girls do not sit together?Solution
6 students can be arranged among themselves in 6P6 ways = 720 ways.
Assume that the 2 girls are one entity. The total number of ways in which they can be arranged among themselves = 2! = 2 ways.
Also, the set of two girls and the other students can be arranged among themselves = 5! = 120 ways.
Thus, total number of ways in which two girls are together = 120 × 2 = 240
Thus, number of ways in which the 2 girls will not sit together = 720 − 240 = 480
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