Find the number of ways of arranging 6 boys and 6 girls in row. In how many of these arrangements.
boys and girls come alternately ?

Explanation

6 boys and 6 girls are altogether 12 persons. They can be arranged in a row in (12)! Ways.
The row may begin with either a boy or a girls, that is 2 ways. If it begins with a boy, then odd places will be occupied by boys and even places by girls. The 6 boys can be arranged in 6 odd places in 6! ways and 6 girls in the 6 even places in 6! ways. Thus the number of arrangements in which boys and girls come alternately is `2xx6!xx6!.`