Combinations and permutation

Both count the ways that (r) objects can be taken from a group of (n) objects, but permutations are arrangements (sequence matters), while combinations are selections (order does not matter). For example, how many ways can you seat people at a table? That's permutation. How many poker hands are available in five-card draw? That's a combination

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Education

Tags:

• Finance
• Quant
• Excel

[YGMH1107]

If they're sitting around a round table as it sounds from your example, then you're answer is wrong It will not be 5P3 since some of the orders will be repeated as there are three ways for Superman to be to the left of the magician for example

[bionicturtledotcom]

@YGMH1107 the table isn't round, you can just look, I don't see how it "sounds" like a round table. But actually, a round table doesn't change the answer: those "shifted" arrangements are simply permutations. So, I disagree with your correction. But feel free to show me what you think the number should be

[YGMH1107]

@bionicturtledotcom My point wasn't that the table is actually a circle! Whatever the shape of the table, there will be people sitting around it and thus ABC can be equal to BCA in terms of position - for example ABC is the same as BCA because B is sitting to the left of A and C is to the right of A in both situations.

The correct answer should have been TWO, there are only two different ways to seat 3 people around a table - ABC and BAC (ACB would be a repeat of the second option

[bionicturtledotcom]

@YGMH1107 your def requires a circular table & ignoring the def of permutation, yes? you need a circular table so BAC equals ACB only bc "B is to the left of C." This in not true for the rectangle. Further, yours needs indifference to the seating position. If 'A' in ABC is next to the heater, then "B" is next to the heater in BAC ... IMO, "permutation" implies seating position matters! So ... i still don't buy your correction but thank you for clarifying why you say so

[bionicturtledotcom]

@YGMH1107 more succinctly, your assertion that "there are only two different ways to seat 3 people around a table" requires assumption(s) that negate the definition of permutation. I would say there are 6 ways to seat 3 people: 3 * 2 * 1, because position matters in a permutation, by definition, as sequence matters. In fact, you do require a circle to nullify this assumption (IMO)!

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