Question
Five students are to be arranged on five chairs for a
photograph. Three of these are girls and the rest are boys. Find out the total number of ways in which three girls are not together.Solution
5 students can be arranged among themselves in 5P5 ways = 120 ways.
Assume that the 3 girls are one entity. The total number of ways in which they can be arranged among themselves = 3! = 6 ways.
Also, the set of three girls and the other students can be arranged among themselves = 3! = 6 ways.
Thus, total number of ways in which three girls are together = 6 × 6 = 36
Thus, number of ways in which all 3 girls will not occupy consecutive seats = 120 − 36 = 84
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