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February 22, 2026, 04:26:19 am
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TonyZ

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Question
« on: November 04, 2009, 06:07:17 pm »
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In how many ways can 7 students be arranged in groups of 3?

The answer from TSFX says it's 7P3...but why does the order matter?...
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2008: Chinese FL [40]
2009: ESL [-], Methods [47], Physics [46], Specialist [49], Uni maths [5.5]
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2010: Commerce @ Melb

krzysiek

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Re: Question
« Reply #1 on: November 04, 2009, 06:38:56 pm »
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I don't understand what it is exactly that you're asking. How many ways can 7 students be arranged in groups of 3 would be, on the TI calculator, 7Cr3, representing - how many groups of 3 can be made with 7, the co-efficient in front of Cr. I assume this is the same case with 7P3?
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TonyZ

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Re: Question
« Reply #2 on: November 04, 2009, 06:46:11 pm »
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cos i think it should be 7C3..
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2008: Chinese FL [40]
2009: ESL [-], Methods [47], Physics [46], Specialist [49], Uni maths [5.5]
ENTER: 99.60
2010: Commerce @ Melb

kamil9876

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Re: Question
« Reply #3 on: November 04, 2009, 06:48:46 pm »
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into groups of 3? what does this mean. That each student must belong to some group? Or that there is only one group that contains 3 of them?  7 is not a multiple of 3 so it is not possible that all everyone can belong to a group of 3, that is if no one student can belong to more than one group.

7C3 is the answer to "how many different ways to put 3 students into one group from 7 students"

3^7 is the answer to "how many different ways are there to split them into 3 groups" (where a group can be empty)
Quote
I assume this is the same case with 7P3?

Don't think so, 4P3=24, 4C3=4. ie: P means order matters, C means order does not matter, so obviously 4C3 is smaller.
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."
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