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In how many ways can the letters AABB be arranged uniquely in a row?

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Joined: 29 Jan 2019
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In how many ways can the letters AABB be arranged uniquely in a row?  [#permalink]

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New post 21 Oct 2019, 06:37
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (00:48) correct 29% (00:46) wrong based on 21 sessions

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In how many ways can the letters AABB be arranged uniquely in a row?

(A) 24
(B) 6
(C) 4
(D) 8
(E) 12
Intern
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Joined: 19 Mar 2019
Posts: 23
Location: India
GPA: 3.7
WE: Engineering (Manufacturing)
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Re: In how many ways can the letters AABB be arranged uniquely in a row?  [#permalink]

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New post 21 Oct 2019, 08:18
Srsrsr32 wrote:
In how many ways can the letters AABB be arranged uniquely in a row?

(A) 24
(B) 6
(C) 4
(D) 8
(E) 12


Since A and B are repeated twice we need to divide by 2! x 2!

4!/2!2! - 6 ways

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Re: In how many ways can the letters AABB be arranged uniquely in a row?  [#permalink]

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New post 21 Oct 2019, 09:32
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Srsrsr32 wrote:
In how many ways can the letters AABB be arranged uniquely in a row?

(A) 24
(B) 6
(C) 4
(D) 8
(E) 12


Let us start with 4 slots for the 4 letters. If we label the letters as A1 A2 and B1 B2, we have 4 possibilities for the first slot and 3 for the second slot since we used up a letter. Then 2x for the third slot etc, and we multiply all these possibilities to get 4*3*2 = 4!. Then we need to eliminate the duplicate combinations because we don't actually differentiate the A's and B's (A1A2 is the same as A2A1 for this question). Therefore divide 4! by 2! to not double count A's and another 2! to not double count B's.

To sum it all up, 4! combinations becasue of 4 slots and 4 choices, divide by 2! for A and 2! for B. 4!/(2!*2!) = 3*2 = 6.

Ans: B
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Re: In how many ways can the letters AABB be arranged uniquely in a row?  [#permalink]

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New post 21 Oct 2019, 10:44
Srsrsr32 wrote:
In how many ways can the letters AABB be arranged uniquely in a row?

(A) 24
(B) 6
(C) 4
(D) 8
(E) 12


Total letters = 4
Repeating = 2 A’s & 2 B’s

Number of arrangements = 4!/(2!*2!) = 24/4 = 6

IMO Option B

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Re: In how many ways can the letters AABB be arranged uniquely in a row?   [#permalink] 21 Oct 2019, 10:44
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In how many ways can the letters AABB be arranged uniquely in a row?

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