
Is this a permutation?
In order to determine the number of strings that can be formed by ordering the letters in "GUIDE", do I do P(6,5) = 6!/1! = 6! = 720 or am I wrong?
If I'm right, please tell me so that I can know otherwise, please tell me what I'm doing wrong and how to do it correctly.
Any help would be greatly appreciated!
Thanks in advance!

Where did you get the 6 from? There are 5 letters in guide...
5!

Using your notation, I want to find all order the letters G,U,I,D,E. So, I wish to find all orderings involving all of the letters. Since there are five letter in GUIDE. So, we use $\displaystyle P(5,5) = 5!$. Or, "5 pick 5", as professors often say.
Now if I wanted all strings of length 3, by ordering the same letters, I would use $\displaystyle P(5,3) = \frac{5!}{(53)!} = 5*4*3 = 60 $. Or rather, "5 pick 3"