Find the number of ways of arranging 6 boys and 6 girls in row. In how many of these arrangements.
no two girls are together

Explanation

6 boys and 6 girls are altogether 12 persons. They can be arranged in a row in (12)! Ways.
First arrange the 6 boys in a row in 6! Ways. Then we can find 7 gaps between them (including the beginning gap and the ending gap) as shown below by the letter. x:

Thus we have 7 gaps and 6 girls. They can be arranged in `""^(7)P_(6)` ways.
Hence, the number of arrangements which no two girls sit together is `6!xx""^(7)P_(6)=7. 6!. 6!`.