In how many ways can the letters of the word LEVEL be arranged so that the first letter is and the last letter is ?
4
6
10
12
24
OA - 6
I see how 3! = 6. That is, fix L and E and then we are left with only 6 possibilities for LEV.
My question is that - why aren't we counting two possibilities of choosing the letters L and E? Essentially, let's consider the following diagram :
1 2 3 4 5
there are two ways one can choose L and E for the first and the last position. Why aren't we counting that?
help?
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Counting question - need expert help
This topic has expert replies
-
voodoo_child
- Master | Next Rank: 500 Posts
- Posts: 405
- Joined: Thu Feb 10, 2011 1:44 am
- Thanked: 3 times
- Followed by:1 members
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
I think you're missing part of the question.voodoo_child wrote:In how many ways can the letters of the word LEVEL be arranged so that the first letter is and the last letter is ?
4
6
10
12
24
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
voodoo_child
- Master | Next Rank: 500 Posts
- Posts: 405
- Joined: Thu Feb 10, 2011 1:44 am
- Thanked: 3 times
- Followed by:1 members
Sorry Bret. There was a copy paste error.
In how many ways can the letters of the word LEVEL be arranged so that the first letter is "L" and the last letter is "E" ?
4
6
10
12
24
In how many ways can the letters of the word LEVEL be arranged so that the first letter is "L" and the last letter is "E" ?
4
6
10
12
24
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
I see.voodoo_child wrote:Sorry Bret. There was a copy paste error.
In how many ways can the letters of the word LEVEL be arranged so that the first letter is "L" and the last letter is "E" ?
4
6
10
12
24
Your earlier question was "Why don't we count the 2 ways to select the L for the first letter and the 2 ways to select the E for the last letter?" Well, there aren't really 2 ways to make L the first letter since both L's in LEVEL are identical. The same goes for selecting an E for the last letter.
It doesn't matter which L you choose and which E you choose. Once those 2 letters are in place, we have L _ _ _ E, and we must fill the 3 spaces with the 3 letters E, V, and L.
We can fill 3 spaces with 3 different letters in 3! ways (6 ways).
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
