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Question
3 boys and 3 girls are to sit in a row. How many ways can this be done if boys and girls are at alternate places
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Solution
Since boys and girls are at alternate places, the 3 boys can occupy 3 odd places (Ist, 3rd, Sth) in 3P3 ways and 3 girls can occupy 3 even places (2nd, 4th, 6th) in 3P3, ways or the 3 boys can occupy 3 even places in 3P3, ways and 3 girls can occupy 3 odd places in 3P3, ways.
Hence, the total number of seating arrangements in which boys and girls are at alternate places.
= 3P3 × 3P3 + 3P3 × 3P3
= 3!3! + 3!3!
= 2 (3!)2
= 2(3 × 2 ×1)2
= 2 × 36
= 72
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