Counting question - need expert help

Expert replies

voodoo_child: Master | Next Rank: 500 Posts; Posts: 405; Joined: Thu Feb 10, 2011 1:44 amFollowed by: 1 member; Thanked: 3 times

by voodoo_child » Mon Jul 02, 2012 5:19 am

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?

Source: Beat The GMAT — Problem Solving | Mon Jul 02, 2012 5:19 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jul 02, 2012 7:47 am

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

I think you're missing part of the question.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

voodoo_child: Master | Next Rank: 500 Posts; Posts: 405; Joined: Thu Feb 10, 2011 1:44 amFollowed by: 1 member; Thanked: 3 times

by voodoo_child » Mon Jul 02, 2012 12:45 pm

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

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jul 02, 2012 1:38 pm

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

I see.
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

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review