In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose a 3 member committee which must have at least one French teacher, how many different committees are possible?

The official answer is 100.

I know that to determine the total possible number of committee combinations I would do the following:

10!/3!7! to get a total of 120 combinations. I don't know how to limit this number to include a French teacher in each group.

Thanks for your help in advance!