A group of 5 kids went to the movie theater. How many different ways can they be seated in an empty row of 7 seats?

We can choose any 5 of the 7 seats for them to sit in. And for each of these choices, there are 5! ways to arrange the children.

So we have...

C(7,5) * 5!  = 2520 ways......

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)

$${\mathtt{5}}{!}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{7}}{!}}{{\mathtt{5}}{!}{\mathtt{\,\times\,}}({\mathtt{7}}{\mathtt{\,-\,}}{\mathtt{5}}){!}}}\right)} = {\mathtt{2\,520}}$$