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# In how many ways can the word "GMAT" be arranged so that no such arran

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Joined: 06 Jun 2014
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In how many ways can the word "GMAT" be arranged so that no such arran  [#permalink]

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Updated on: 07 Mar 2016, 05:03
1
5
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:57) correct 25% (01:05) wrong based on 221 sessions

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In how many ways can the word "GMAT" be arranged so that no such arrangement has A as the first letter?

A. 6
B. 12
C. 18
D. 24
E. 30

Originally posted by vinoo7 on 07 Mar 2016, 05:00.
Last edited by Bunuel on 07 Mar 2016, 05:03, edited 1 time in total.
RENAMED THE TOPIC.
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Re: In how many ways can the word "GMAT" be arranged so that no such arran  [#permalink]

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07 Mar 2016, 05:07
2
Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6

Number of ways of arranging GMAT so that A is not in the beginning = 24 - 6 = 18

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Re: In how many ways can the word "GMAT" be arranged so that no such arran  [#permalink]

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07 Mar 2016, 05:38
1st letter can be arranged in 3 ways (GMT - leaving A)
2nd letter can be arranged in 3 ways again (including A)
3rd letter can be arranged in 2 ways
4th in one way
total no. of ways = 3*3*2=18

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Re: In how many ways can the word "GMAT" be arranged so that no such arran  [#permalink]

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07 Mar 2016, 10:05
2
vinoo7 wrote:
In how many ways can the word "GMAT" be arranged so that no such arrangement has A as the first letter?

A. 6
B. 12
C. 18
D. 24
E. 30

Another approach:

When we check the answer choices (NOTE: Always check the answer choices before trying to solve any Problem Solving question), we see that the answer choices are relatively small. So, we might consider LISTING and COUNTING the possible outcomes.
If we start by listing all possible outcomes where B is the first letter, we get:
- BGAT
- BGTA
- BTAG
- BTGA
- BAGT
- BATG
Note: So far, we have 6 outcomes where B is the first letter.
At this point, I might recognize that, we will get 6 more outcomes if we make T the first letter, and we will get 6 more outcomes if we make G the first letter.

So, the total number of outcomes = 6 + 6 + 6 = 18

For more on this LISTING and COUNTING approach, watch this free video:
- Listing and counting: https://www.gmatprepnow.com/module/gmat ... /video/773

Cheers,
Brent
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Re: In how many ways can the word "GMAT" be arranged so that no such arran  [#permalink]

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05 Oct 2018, 09:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In how many ways can the word "GMAT" be arranged so that no such arran   [#permalink] 05 Oct 2018, 09:56
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