Question: Let us return to sugar-numbers for a moment.
(a) Pull a sugar-number out of the bag of n sugar-numbers. How many ways are there to do this?
(b) Now pull another sugar-number out of the bag and put it next to the first sugar-number. How many ways are there to do this?
(c) Keep pulling sugar-numbers out of the bag until you have a line of k sugar-numbers. How many ways are there to produce this line?
(d) Basically, you have chosen k sugar-numbers from a bag of n sugar n umbers. But your resulting number of ways to do this is not the same as 
. (If you don't believe this, check for a few values of n and k.) What information do you need to take into consideration? Do so.
(e) Rewrite your expression so that it only uses factorials. Now you have a handy formula for computing .! (No, not "n-choose-k-factorial." This is the interjection sort of exclamation point.)