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In how many ways can 6 boys be seated in a row such that two boys (Ashok and Pankaj) are never seated together.

In how many ways can 6 boys be seated in a row such that two boys (Ashok and Pankaj) are never seated together. Correct Answer 480

Concept:-

For these kind of questions we take the number of ways in which they are seated together and subtract them from the total number of ways.

Calculation:-

Number of ways of seating 6 boys in a row = 6! = 720

Number of ways in which Ashok and Pankaj are sitting together can be found by taking both of them as 1.

So number of ways both of them are sitting together = (AP + 4)! + (PA + 4)! = 5! × 2 = 240

Total number of ways = 720 - 240 = 480

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