how many ways can the letters of the following words be arranged?
= Level
= Trust
= School
= Rules
word combination....
This topic has expert replies

 Master  Next Rank: 500 Posts
 Posts: 148
 Joined: 10 Dec 2008
 Location: SF, CA
 Thanked: 12 times
For 5letter 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 4letter 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 6letter words.
Because you have 5 spots for the 1st letter, then 4 spots for the second letter, etc.
For 4letter 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 6letter words.
The more you look, the more you see.

 GMAT Instructor
 Posts: 1223
 Joined: 01 May 2008
 Location: Los Angeles, CA
 Thanked: 185 times
 Followed by:15 members
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.
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.
Jim S.  GMAT Instructor  Veritas Prep