# Math Help - [SOLVED] permutations

1. ## [SOLVED] permutations

At the Olympics, there are four french judges, six Spanish judges and seven German judges. How many ways are there of sitting them in a row if judges of the same nationality are grouped together?

I was thinking designating letters so ffffssssssggggggg

$\frac{17!}{4!6!7!}$

what do you think?

2. Try $(3!)(4!)(6!)(7!)$. Can you explain why?
Remember, they sit together.

3. Originally Posted by Plato
Try $(3!)(4!)(6!)(7!)$. Can you explain why?
Remember, they sit together.
Thanks Plato yes I can, see if we had ffffssssssggggg we would have 3! for each 3! ways they can be changed multiplied by the amount of judges from the different nationalities.