7P5 ways put it into the web2 calc as
nPr(7,5)
$${\left({\frac{{\mathtt{7}}{!}}{({\mathtt{7}}{\mathtt{\,-\,}}{\mathtt{5}}){!}}}\right)} = {\mathtt{2\,520}}$$
This means how many permutations of 5 objects can be chosen from 7 objects (order matters)
or you could say that there are 5! ways to order the childrens and for each of those there is 7C5 ways that the seats can be choosen (ah that is the way CPhill looked at it)
5! * 7C5
enter the web2 calc as 5!*nCr(7,5)
$${\mathtt{5}}{!}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{7}}{!}}{{\mathtt{5}}{!}{\mathtt{\,\times\,}}({\mathtt{7}}{\mathtt{\,-\,}}{\mathtt{5}}){!}}}\right)} = {\mathtt{2\,520}}$$
.