Problem Solving

how many ways can the letters of the following words be arranged?

= Level
= Trust
= School
= Rules

For 5-letter words you need to calculate=5*4*3*2*1=120
Because you have 5 spots for the 1st letter, then 4 spots for the second letter, etc.
For 4-letter words you need to calculate=4*3*2*1=24
The same logic applies as the one stated above.
And use the same logic for 6-letter words.

Don't forget that you also need to divide by n!, where "n" is the number of times a letter repeats itself in the word. So, for example, SCHOOL would be:

6! / 2!

Since there are two "O"s.

So, if we had a word such as "ASSESS", that would be:

6! / 4!

Since the "S" repeats itself four times.

It gets even weirder if you have multiple letters that repeat, such as RECESS - both the "E" and the "S" repeat twice. So, we would have:

6! / (2!*2!)

I can't say I've ever seen one of these on the real GMAT, but it's handy to know.