How many different pairs can be selected from a group of 7 people?
The answer is 21?
I just can't understand why to divide at the 2 at th end?!
Thank you
Why to divide by 2?
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Why, or rather what says to divide by 2 at the end?white wrote:How many different pairs can be selected from a group of 7 people?
The answer is 21?
I just can't understand why to divide at the 2 at th end?!
Thank you
Just write out the numbers 1 to 7 and start pairing them together It should be quick enough and you should see a patern develop and probably won't need to even write it all the way out.
Possible pairs
1-2, 1-3, 1-4, 1-5, 1-6, 1-7
2-3, 2-4, 2-5, 2-6, 2-7
3-4, 3-5, 3-6, 3-7
4-5, 4-6, 4-7
5-6, 5-7
6-7
21 pairs
Given 7 people(A,B...G), we don't care if A is chosen first or last.
We have to eliminate those redundancies. How many of those? 2.
The equation is (if order matters)
7!/(7-2)! = 7! / 5!
If order matters not(our case), we have to divide by 2 (pair)
7! / ( (7-2)! * 2) = 7! /(5! * 2) = 7*6 / 2 = 21
We have to eliminate those redundancies. How many of those? 2.
The equation is (if order matters)
7!/(7-2)! = 7! / 5!
If order matters not(our case), we have to divide by 2 (pair)
7! / ( (7-2)! * 2) = 7! /(5! * 2) = 7*6 / 2 = 21
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We need to divide by 2 because you calculate EACH pair by this formula:
7!/5!=42
If you'd have a set of letters ABCDEFG and AB would be different from BA, then the 42 pairs would be correct. But here a pair of two people does not change depending on whether you pick one person first and the other person second, then will still be a pair. This is why you're counting those pairs twice and need to divide by 2:
7!/5!2!=21
7!/5!=42
If you'd have a set of letters ABCDEFG and AB would be different from BA, then the 42 pairs would be correct. But here a pair of two people does not change depending on whether you pick one person first and the other person second, then will still be a pair. This is why you're counting those pairs twice and need to divide by 2:
7!/5!2!=21
The more you look, the more you see.
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Technically, you're dividing by 2! (2 factorial), not 2. I think it's better to think of it as the factorial so that you can answer other, similar questions such as:
How many teams of 3 people can you make out of 7 possible choices?
That would be:
(7x6x5)/(3x2x1) = 35
The way I like to think about it is - in very non-mathematical terms - if order doesn't matter, count up up the number of items in your numerator, call that number "n", and divide by n!.
How many teams of 3 people can you make out of 7 possible choices?
That would be:
(7x6x5)/(3x2x1) = 35
The way I like to think about it is - in very non-mathematical terms - if order doesn't matter, count up up the number of items in your numerator, call that number "n", and divide by n!.
Jim S. | GMAT Instructor | Veritas Prep