Asked by Beth
Any 2 points determine a line. If there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determined by pairs of these 6 points?
The answer key says 15, and the explanation is (6!)/(2!4!). Could someone explain to me why there is a 6, 2, and 4 factorials and how to approach this question please?
The answer key says 15, and the explanation is (6!)/(2!4!). Could someone explain to me why there is a 6, 2, and 4 factorials and how to approach this question please?
Answers
Answered by
Bosnian
Paste your question in google.
You will find couple explanations.
You will find couple explanations.
Answered by
Reiny
This type of question often comes up when you study
"permutations" and "combinations"
You clearly must be studying permutations and combinations
In this case you are "choosing" any 2 of the 6 points
choose ----> combinations, (the order in which you choose any 2 points does not matter)
e.g. AB or BA yields the same line
the definition of C(n,r) is n!/(r!(n-r)!) , see your text
and we have to choose 2 from 6
= C(6,2) = 6!/(2!4!) = 15
"permutations" and "combinations"
You clearly must be studying permutations and combinations
In this case you are "choosing" any 2 of the 6 points
choose ----> combinations, (the order in which you choose any 2 points does not matter)
e.g. AB or BA yields the same line
the definition of C(n,r) is n!/(r!(n-r)!) , see your text
and we have to choose 2 from 6
= C(6,2) = 6!/(2!4!) = 15
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