The number of ways in which 6 boys and 7 girls can sit in a row such that

“They sit alternately is”

$\underset{\_}{\text{G}}\text{B}\underset{\_}{\text{G}}\text{B}\underset{\_}{\text{G}}\text{B}\underset{\_}{\text{G}}\text{B}\underset{\_}{\text{G}}\text{B}\underset{\_}{\text{G}}\text{B}\underset{\_}{\text{G}}$

Now arrange 7 girls in the 7 gaps in ${}^7{P}_7$  ways

$\therefore$  Required number of ways $=7!6!$