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

Answer 1

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