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

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19 Jul 2017, 21:32

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95% (hard)

Question Stats:

44% (01:19) correct 56% (02:13) wrong based on 97 sessions

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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?

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?

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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Re: Alice, Bobby, Cindy, Daren and Eddy participate in a marathon. If each [#permalink]

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22 Jul 2017, 23:33

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?

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.

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

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23 Jul 2017, 00:37

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?

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 !