Twenty-one dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle? Pick.
A) 1299
B) 1305
C) 1311
D) 1317
E) 1323
The total number of ways we can choose three dots is 21C3=1330.   We can form seven equilateral triangles from these twenty-one dots.   There are  1330 - 7= 
<gadget id="calculator"> 1330 - 7</gadget>
<output>1_323</output>
1323 combinations which do not form an equilateral triangle.   The answer is 1323.
<result>E</result>
Twenty-one dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle?