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'A' comes before 'D' in the word 'AUDIT'

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kumaran14
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'A' comes before 'D' in the word 'AUDIT' [#permalink] New post   Updated on: 04 Jul 2020, 11:18
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In how many different ways can the letters of the word 'AUDIT' be arranged in such a way that 'A' comes before 'D' ?

(A) 72
(B) 60
(C) 48
(D) 44
(E) 30
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B

Originally posted by kumaran14 on 04 Jul 2020, 05:25.
Last edited by GreenlightTestPrep on 04 Jul 2020, 11:18, edited 2 times in total.
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Re: 'A' comes before 'D' in the word 'AUDIT' [#permalink] New post   04 Jul 2020, 11:25
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kumaran14 wrote:
In how many different ways can the letters of the word 'AUDIT' be arranged in such a way that 'A' comes before 'D' ?

(A) 72
(B) 60
(C) 48
(D) 44
(E) 30


The key concept here is that, for every arrangement in which 'A' comes before 'D', there is an arrangement in which 'D' comes before 'A'
In other words, in HALF of the arrangements, 'A' comes before 'D' and in HALF of the arrangements, 'D' comes before 'A'

To better understand what I mean, let's look at a smaller example:
Let's list all 6 arrangements of the letters in the word BAD:
ABD
ADB
BAD
BDA
DAB
DBA
In the first three arrangements, 'A' comes before 'D'
In the last three arrangements, 'D' comes before 'A'


The same applies to the five letters in the word AUDIT
We can arrange the five letters in 5! ways (= 120 ways)
In HALF of those 120 arrangements, 'A' comes before 'D'

120/2 = 60

Answer: B

Cheers,
Brent
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kumaran14
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Re: 'A' comes before 'D' in the word 'AUDIT' [#permalink] New post   04 Jul 2020, 08:00
can you please explain further ?
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Re: 'A' comes before 'D' in the word 'AUDIT' [#permalink] New post   04 Jul 2020, 11:00
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You do have 5 letters . As such the combinations are

\(5 \times 4 \times 3 \times 2 \times 1\)

However, you need to divide by 2 because you do have two scenarios: one in which the two letters are close and one in which they are not

\(\frac{120}{2}=60\)

B should be the answer
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Re: 'A' comes before 'D' in the word 'AUDIT' [#permalink] New post   10 Jul 2020, 08:35
GreenlightTestPrep wrote:
kumaran14 wrote:
In how many different ways can the letters of the word 'AUDIT' be arranged in such a way that 'A' comes before 'D' ?

(A) 72
(B) 60
(C) 48
(D) 44
(E) 30


The key concept here is that, for every arrangement in which 'A' comes before 'D', there is an arrangement in which 'D' comes before 'A'
In other words, in HALF of the arrangements, 'A' comes before 'D' and in HALF of the arrangements, 'D' comes before 'A'

To better understand what I mean, let's look at a smaller example:
Let's list all 6 arrangements of the letters in the word BAD:
ABD
ADB
BAD
BDA
DAB
DBA
In the first three arrangements, 'A' comes before 'D'
In the last three arrangements, 'D' comes before 'A'


The same applies to the five letters in the word AUDIT
We can arrange the five letters in 5! ways (= 120 ways)
In HALF of those 120 arrangements, 'A' comes before 'D'

120/2 = 60

Answer: B

Cheers,
Brent


i assumed A and D to be 1 letter

so we have 4 letters, with 4! ways to arrange them then i multplied by 2, getting 48. can someone explain?
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Re: 'A' comes before 'D' in the word 'AUDIT' [#permalink] New post   10 Jul 2020, 09:11
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georgekaterji wrote:
i assumed A and D to be 1 letter

so we have 4 letters, with 4! ways to arrange them then i multplied by 2, getting 48. can someone explain?


A and D don't have to be adjacent (i.e., one letter)

So, for example, the following meet the condition that A comes before D.

AuidT
AuTdi
ATuid
AudTi
etc
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Re: 'A' comes before 'D' in the word 'AUDIT' [#permalink] New post   11 Sep 2024, 16:05
GreenlightTestPrep wrote:
kumaran14 wrote:
In how many different ways can the letters of the word 'AUDIT' be arranged in such a way that 'A' comes before 'D' ?

(A) 72
(B) 60
(C) 48
(D) 44
(E) 30


The key concept here is that, for every arrangement in which 'A' comes before 'D', there is an arrangement in which 'D' comes before 'A'
In other words, in HALF of the arrangements, 'A' comes before 'D' and in HALF of the arrangements, 'D' comes before 'A'

To better understand what I mean, let's look at a smaller example:
Let's list all 6 arrangements of the letters in the word BAD:
ABD
ADB


How D COmes Before A?
BAD
BDA
DAB
DBA
In the first three arrangements, 'A' comes before 'D'
In the last three arrangements, 'D' comes before 'A'


The same applies to the five letters in the word AUDIT
We can arrange the five letters in 5! ways (= 120 ways)
In HALF of those 120 arrangements, 'A' comes before 'D'

120/2 = 60

Answer: B

Cheers,
Brent
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Re: 'A' comes before 'D' in the word 'AUDIT' [#permalink] New post   24 Dec 2025, 02:07
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Re: 'A' comes before 'D' in the word 'AUDIT' [#permalink]
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