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Apr 2808:00 AM PDT
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Louis14
Joined: 01 Nov 2019
Last visit: 04 Nov 2023
Posts: 249
Own Kudos:
Given Kudos: 472
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
GPA: 3.56
14 Jul 2020, 05:02
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I have been studying combinations and permutations for a while now but I just recently created some conceptual situations in my head that I have tried to answer satisfactorily but still to no avail. I will try to put out what's in my mind. Please bear with me because there few eerie conceptual questions that I have been trying to understand. I shall highly appreciate your help.
So, here we go..
If we have a set of 11 elements, and some of the elements are repeated in the set, how can we find 11P3 and 11C3, if it's possible in the first place? For example, say we have the word MISSISSIPPI, how will we find 11P3 and 11C3 from the word MISSISSIPPI?
The things that's bothering me is the question that 'can we make combinations out of a larger set that does not have distinct elements or MUST all the elements of the set be distinct for us to make combinations?'
If we have a set, say, DDDDDXXX, what will be the number of permutations of this set? What will be 8C3 of this set? Would they be the same i.e. 8!/5!3!? If we were to find 8P3 of this set, what would that be?
I know these are lot of questions, and again, I shall very highly appreciate your help in making me answer these questions. Thanks in advance.
So, here we go..
If we have a set of 11 elements, and some of the elements are repeated in the set, how can we find 11P3 and 11C3, if it's possible in the first place? For example, say we have the word MISSISSIPPI, how will we find 11P3 and 11C3 from the word MISSISSIPPI?
The things that's bothering me is the question that 'can we make combinations out of a larger set that does not have distinct elements or MUST all the elements of the set be distinct for us to make combinations?'
If we have a set, say, DDDDDXXX, what will be the number of permutations of this set? What will be 8C3 of this set? Would they be the same i.e. 8!/5!3!? If we were to find 8P3 of this set, what would that be?
I know these are lot of questions, and again, I shall very highly appreciate your help in making me answer these questions. Thanks in advance.
14 Jul 2020, 05:15
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Louis14
CONCEPT 1 : \(nP^r = nC^r*r!\)
CONCEPT 2 : \(nC^r\) is used where the selection of a few items from a bigger number is needed and Arrangement is not relevant
CONCEPT 3 : \(nC^r*r!\) is used where the selection of a few items from a bigger number is needed AS WELL AS Arrangement is to be done
e.g. If you need to pick 2 T-shirts out of 5 to pack in a bag the answer is \(5C^3\) BUT
If you need to wear 2 distinct T-shirts out of 5 on two days to be dressed differently then dressing outcomes = \(5C^3*3! = 5P3\)
Suggestion: AVOID using \(nP^r\)
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Louis14
Joined: 01 Nov 2019
Last visit: 04 Nov 2023
Posts: 249
Own Kudos:
Given Kudos: 472
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
GPA: 3.56
14 Jul 2020, 06:56
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GMATinsight
I guess you wanted to say 5C2 instead of 5C3 because we are choosing 2 shirts.
