Here are some notations for this thing...

We use "P" for "permutation":

n P r  =  P^( n ) r  =  P( n , r )  =  n! / ( n - r )!

Look for one of these on your calculator...  Now, try your calculator with the last two problems.

(You usually put the n guy in first, then hit the button, then put the r guy in and hit  = .)

* Again, it's better to figure these guys out with slots than to just try to
  memorize a formula!

Why?  Because sometimes you have to think...  and you need the practice!

Check it out:

You have 9 boys and 12 girls.  You're going to take 4 boys and 3 girls and arrange them in a line boy - girl - boy - girl.  How many ways can you do it?

Let's do the slot thing:


b__  g__  b__  g__  b__  g__  b__

Let's do the boys first...

b 9   g__   b 8   g__   b 7   g__   b 6

Get it?

Now, you fill in the girls and finish it off:

b 9   g__   b 8   g__   b 7   g__   b 6  =  _______