BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Another one in Perm & Comb

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Thu Jun 23, 2011 9:32 am
Location: Bangalore, India
Thanked: 2 times
Followed by:1 members

Another one in Perm & Comb

by vabhs192003 » Mon Dec 10, 2012 12:19 pm
Hello,

I have a conceptual problem in application in the below question.

Q. How many words can be made from the word IMPORTANT,using all the 9 alphabets, in which both the Ts do not come together, ?
a) 141130
b) 141210
c) 113311
d) 888222
e) 141120

OA: "e".

The problem is I am unable to understand why I can't apply the rule of Permuted selection here. As in, rearranging the alphabets as : _ I _ M _ P _ O _ R _ A _ N _. So , we have alphabets I,M,P,O,R,A,N which can be rearranged in 7! ways and the two T's can be seated in any of the 8 _ spaces in the above by selecting any two via permutation as: 8P2. so the answer would be 7! x 8P2. But this does not give me the correct answer. Does it mean that Permutation selection can't be done when the objects are similar like two T's in our case. But again isnt it the case of selecting from 8 different spaces taking 2 at a time,hence 8P2, which is inline with permuted selection definition.
Experts please correct me wherever I am going wrong.
Top
Source: — Problem Solving |
User avatar
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Thu Jun 23, 2011 9:32 am
Location: Bangalore, India
Thanked: 2 times
Followed by:1 members

by vabhs192003 » Mon Dec 10, 2012 12:47 pm
OK.
I think I have realized my mistake. The approach was right I guess, except that I missed: 8P2/2! which gives me my answer.
Never the less I would like to see other approaches to the question.

Thanks.
Top

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Mon Dec 10, 2012 12:55 pm
vabhs192003 wrote:Hello,

I have a conceptual problem in application in the below question.

How many words can be made from the word IMPORTANT,using all the 9 alphabets, in which both the Ts do not come together, ?
a) 141130
b) 141210
c) 113311
d) 888222
e) 141120
OA: "e".
Here's one approach.

First ignore the restriction that says the T's cannot be adjacent to one another. So, we have 9 objects (letters) and we want arrange all of them.

Note: When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:

If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]

In this question, the word IMPORTANT has two identical letters (the T's), so when we apply the MISSISSIPI rule, we see that the letters in IMPORTANT can be arranged in 9!/2! ways.

Now at this point, we've ignored the restriction that says the T's cannot be adjacent to one another.

So, from the 9!/2! possible words, we need to subtract all of the words in which the T's are adjacent. How many such words are there?

To find out, let's "glue" the two T's together, to get one symbol "TT." This will ensure that the letters are adjacent.
So, we want to determine how many ways we can arrange the following 8 "letters": I, M, P, O, R, A, N, TT
This can be accomplished in 8! ways. Notice that all 8! words will have the two T's adjacent.

So, the total number of words in which the T's are not adjacent = 9!/2! - 8! = [spoiler]141,120 = E[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Thu Jun 23, 2011 9:32 am
Location: Bangalore, India
Thanked: 2 times
Followed by:1 members

by vabhs192003 » Mon Dec 10, 2012 1:01 pm
Thanks Brent. I knew the rule of permutation of n things not all different. But was confused when I couldn't reach the expected answer. Your approach is also straight forward.
Top
Post new topic Post Reply
• Page 1 of 1