Question

There are three boys and three girls at a party. in how many ways can they be seated in a row if they must sit alternating boys and girls?

Answer 1

The number of permutations of the three girls is 3P3 = 6. Similarly the number of permutations of the boys is 6. Each permutation of girls can be taken with each permutation of boys. Additionally each arrangement from left to righr can have a girl first or a boy first.
Total number of ways is given by:
$6\times6\times2=72\ ways$