Asked by jennifer
Five points lie in the same plane with no three points on the same line. A circle can be drawn through any three of the five points. What is the total number of different circle that can be drawn such that each circle passes through three of the five points?
Answers
Answered by
Damon
how many combinations of three from 5
n!/[ r!(n-r)! ]
5!/[2!(3!)] = 10
or do one by 1 the hard way
A B - C, D, E --> 3
A C - D, E -->2
A D - E -->1
B C - D, E -->2
B D - E -->1
C D - A -->1
3+2+1+2+1+1 = 10
n!/[ r!(n-r)! ]
5!/[2!(3!)] = 10
or do one by 1 the hard way
A B - C, D, E --> 3
A C - D, E -->2
A D - E -->1
B C - D, E -->2
B D - E -->1
C D - A -->1
3+2+1+2+1+1 = 10
Answered by
Reiny
Since no choice of 3 points forms a straight line, you are simply finding the number of ways to choose 3 of the 5 points, which is
C(5,3) or 5!/(3!2!) = 10
C(5,3) or 5!/(3!2!) = 10
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