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# Given the 6 letter word SQUARE, how many permutations are

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CEO
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Given the 6 letter word SQUARE, how many permutations are [#permalink]

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28 Nov 2007, 14:30
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Given the 6 letter word SQUARE, how many permutations are there where QUE are next to each other?
Senior Manager
Joined: 26 Jul 2007
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28 Nov 2007, 14:35
24?

If QUE is at the beginning, there are 3! possibilities of SUA.
IF one letter is before QUE and two are after, there are 3! possibilities of SUA.
If two letters are before QUE and one is after, there are 3! possibilities of SUA.
If QUE is at the end, there are 3! possibilities of SUA.

3! x 4 = 6 x 4=24.

What's the OA?
Intern
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28 Nov 2007, 19:38

6c3/2

whats the OA
Intern
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28 Nov 2007, 20:25
Consider QUE as one alphabet then you have

QUE and S, A, R (4 alphabets to play with)

So 4! = 24
Director
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28 Nov 2007, 22:15
shubhampandey wrote:
Consider QUE as one alphabet then you have

QUE and S, A, R (4 alphabets to play with)

So 4! = 24

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28 Nov 2007, 22:22
I got 24 as well. 4x1!x4!

Is it safe to assume that QUE must be in that same order? because if not answer is 180.
CEO
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29 Nov 2007, 07:46
bmwhype2 wrote:
Given the 6 letter word SQUARE, how many permutations are there where QUE are next to each other?

I made up this question so please correct me if I am wrong.

6 - 3 + 1 = 4!

3 arrangements of QUE = 3!

3! * 4! = 6 * 24 = 144
CEO
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Location: New York City
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Kudos [?]: 943 [0], given: 4

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29 Nov 2007, 07:49
Here is a harder one...

How many ways can we make QES next to each other and R the third letter?
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29 Nov 2007, 08:29
bmwhype2 wrote:
bmwhype2 wrote:
Given the 6 letter word SQUARE, how many permutations are there where QUE are next to each other?

I made up this question so please correct me if I am wrong.

6 - 3 + 1 = 4!

3 arrangements of QUE = 3!

3! * 4! = 6 * 24 = 144

I misunderstood. I thought that QUE had to stay in the order QUE. If QUE can be arranged in any order, then you are correct.
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29 Nov 2007, 16:05
bmwhype2 wrote:
Here is a harder one...

How many ways can we make QES next to each other and R the third letter?

2! * 3! = 12
What do you think?
29 Nov 2007, 16:05
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