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Permutation and Combination - Arranging Speakers with Conditions

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TheBipedalHorse
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Permutation and Combination - Arranging Speakers with Conditions [#permalink] New post   Updated on: 26 Apr 2022, 08:09
The CEO, CTO, and COO of a company along with 5 more people are set to address a gathering of MBA students.

CONDITIONS:

CEO has to speak before CTO
CTO has to speak before the COO

In how many ways can the organizers arrange the sequence of speaking by the 8 speakers?

Answer unknown but a friend of mine suggested 8C3 * 5! as the answer, which I dont know how she came up with

Originally posted by TheBipedalHorse on 26 Apr 2022, 07:13.
Last edited by TheBipedalHorse on 26 Apr 2022, 08:09, edited 1 time in total.
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rprasad6310
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Re: Permutation and Combination - Arranging Speakers with Conditions [#permalink] New post   26 Apr 2022, 07:52
Is the answer : Option C? When do we get OA?
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TheBipedalHorse
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Re: Permutation and Combination - Arranging Speakers with Conditions [#permalink] New post   26 Apr 2022, 08:08
What do you mean by option C? I dont have the correct answer with me but a friend of mine suggested 8C3 * 5! as the answer
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Re: Permutation and Combination - Arranging Speakers with Conditions [#permalink] New post   26 Apr 2022, 08:22
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You could just imagine arranging the 8 people in a random order, and ask: what is the probability the CEO will come before the CTO, and the CTO before the COO? That probability is 1/6, because there are 6 orders the CEO, CTO and COO could end up speaking in, and each of those 6 orders is equally likely. So in 1/6 of all of the orders we could make, the CEO, CTO and COO will end up speaking in that order, and the answer is 8!/6.
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Re: Permutation and Combination - Arranging Speakers with Conditions [#permalink] New post   26 Apr 2022, 08:26
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And that's the same answer as your friend got -- your friend might have thought of it this way: "we have 8 slots on the speaking schedule to fill, and we can choose three of them for the CEO, CTO and COO in 8C3 ways. Once we choose those slots the sequence is predetermined: the CEO goes in the first slot we choose, the CTO in the next, the COO in the last. Then there are 5 slots left to fill using the other five people, and we have 5 choices for the first, 4 for the next, and so on, and the answer is 8C3 * 5!." That also gives the answer.
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Permutation and Combination - Arranging Speakers with Conditions [#permalink] New post   26 Apr 2022, 08:29
Ian, your answer makes sense! Thanks for sharing a new insight - combining probability and combinations to figure out the problem!
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Re: Permutation and Combination - Arranging Speakers with Conditions [#permalink] New post   26 Apr 2022, 08:30
8C3 * 5! is the correct answer..Thanks,,
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Re: Permutation and Combination - Arranging Speakers with Conditions [#permalink]
26 Apr 2022, 08:30
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