SOLUTION: There are 2 red, 5 green, 3 blue, and 4 white points on a circle. Find the number of line segments which have vertices of different colors at the given points.

Question 1205744: There are 2 red, 5 green, 3 blue, and 4 white points on a circle. Find the number of line segments which have vertices of different colors at the given points.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The points on the circle are 2 red (R), 5 green (G), 3 blue (B), and 4 white (W). That's a total of 14 points.

The segments that can be drawn between different color points are...

RG: 2*5 = 10
RB: 2*3 = 6
RW: 2*4 = 8
GB: 5*3 = 15
GW: 5*4 = 20
BW: 3*4 = 12

total: 10+6+8+15+20+12 = 71

ANSWER: 71

To check this answer, we can find the number of segments that can be drawn between points of the same color. Those segments, plus the 71 segments between points of different colors, should be the total number of segments between any two points.

RR: C(2,2) = 1
GG: C(5,2) = 10
BB: C(3,2) = 3
WW: C(4,2) = 6

total between two points of the same color: 1+10+3+6 = 20

total between any two points: 71+20 = 91

total between any two of the 14 points: C(14,2) = 91

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