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# Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each

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Intern
Joined: 11 Jul 2016
Posts: 25
Location: Thailand
GMAT 1: 700 Q48 V38
Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each  [#permalink]

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19 Jul 2017, 22:32
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Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each of them finishes the marathon and no two or three athletes finish at the same time, in how many different possible orders can the athletes finish the marathon so that Alice finishes before Bobby and Bobby before Cindy?

A) 18
B) 20
C) 24
D) 30
E) 36

Source - Math Revolution

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Intern
Joined: 20 Jul 2017
Posts: 2
Re: Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each  [#permalink]

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20 Jul 2017, 02:58
1
Without any constrains there a 5! combinations,

The constraints removes 2 degrees of freedom so 3!

the answer is 5!/3!= 5*4= 20
Math Expert
Joined: 02 Aug 2009
Posts: 6292
Re: Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each  [#permalink]

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20 Jul 2017, 03:07
ssr300 wrote:
Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each of them finishes the marathon and no two or three athletes finish at the same time, in how many different possible orders can the athletes finish the marathon so that Alice finishes before Bobby and Bobby before Cindy?

A) 18
B) 20
C) 24
D) 30
E) 36

Source - Math Revolution

All 5 can be arranged in 5! Ways but without any conditions..
But A,B and C can be arranged in 3! Amongst themselves and ONLY one out of the 3! Will have ABC in that order amongst themselves.
So divide all by 3! $$\frac{5!}{3!}$$=20
B
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 16 Feb 2017
Posts: 25
Re: Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each  [#permalink]

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23 Jul 2017, 00:33
chetan2u wrote:
ssr300 wrote:
Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each of them finishes the marathon and no two or three athletes finish at the same time, in how many different possible orders can the athletes finish the marathon so that Alice finishes before Bobby and Bobby before Cindy?

A) 18
B) 20
C) 24
D) 30
E) 36

Source - Math Revolution

All 5 can be arranged in 5! Ways but without any conditions..
But A,B and C can be arranged in 3! Amongst themselves and ONLY one out of the 3! Will have ABC in that order amongst themselves.
So divide all by 3! $$\frac{5!}{3!}$$=20
B

hi chetan,

why do we need to divide by 3! ?
can you explain in more detail please.

thanks!
Intern
Joined: 15 Jun 2013
Posts: 2
Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each  [#permalink]

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23 Jul 2017, 01:37
GMATAspirer09 wrote:
chetan2u wrote:
ssr300 wrote:
Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each of them finishes the marathon and no two or three athletes finish at the same time, in how many different possible orders can the athletes finish the marathon so that Alice finishes before Bobby and Bobby before Cindy?

A) 18
B) 20
C) 24
D) 30
E) 36

Source - Math Revolution

All 5 can be arranged in 5! Ways but without any conditions..
But A,B and C can be arranged in 3! Amongst themselves and ONLY one out of the 3! Will have ABC in that order amongst themselves.
So divide all by 3! $$\frac{5!}{3!}$$=20
B

hi chetan,

why do we need to divide by 3! ?
can you explain in more detail please.

thanks!

We need to divide by 3! in order to ensure that ABC order is maintained.
If we don't divide by 3 ! then ABC will be arranged in 3! ways = BAC, CAB, CBA , etc .AND we don't want this. We just want ABC order. so In order to ensure that arrangement be only in ABC , we need to divide it by 3 !
Intern
Joined: 03 Dec 2016
Posts: 33
Re: Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each  [#permalink]

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23 Jul 2017, 02:54
1
Shouldn't the answer be just 6?

Considering "ABC" as one set, where have 3 things to arrange"ABC","D" and "E", which can be arranged in 6 ways

Here are the 6 sets:

D ABC E
E ABC D
D E ABC
E D ABC
ABC D E
ABC E D
Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each  [#permalink]

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01 Nov 2017, 09:05
Novice90 wrote:
Shouldn't the answer be just 6?

Considering "ABC" as one set, where have 3 things to arrange"ABC","D" and "E", which can be arranged in 6 ways

Here are the 6 sets:

D ABC E
E ABC D
D E ABC
E D ABC
ABC D E
ABC E D

Question stem says , A should be before B and B should be before C. It doesnot says they all come in line.

So possible combinations:

A B C D E
A B C E D
A D B C E
A E B C D
A B D E C
A B E D C
..... and so on.

Total will be 20 possible orders.

Manager
Joined: 01 Feb 2017
Posts: 146
Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each  [#permalink]

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01 Nov 2017, 16:30
Order for slotting A,B,C is fixed i.e.1.

But Order for D&E is not under any constraint and hence is 5P2.

(Position of A-B-C will be moved, retaining their constrained order, to accommodate D&E in any slot from 5P2).

Therefore, Total Possible Orders of arrangements are=
1x5P2 = 20.

Hence, Ans B

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Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each &nbs [#permalink] 01 Nov 2017, 16:30
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