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Vreddy, don't waste time to be around. I guess other ppl would not try. Based on your approach, I agree with you on the answer. However, the solution in book is slightly different. Select any one of the eight points. The probability that all of the other points lie in the semicircle clockwise from that point is 1/2^7. Since that can be true for at most one of the eight points, the probability that it happens at all is 8/2^7, or 1/16. More generally, the probability that n points lie on a semicircle is n/2^(n-1). **PS I can see that Q1Q1, Q2Q2, Q3Q3 and Q4Q4 are also counted from the soln.

8 points are selected at random on a circle, what is the probability they lie on a semicircle?

Vreddy, you are right. I have seen that you left for awhile and back to solve it. Thanks.

Let N be the greatest integer multiple of 8, no two of those digits are the same. What is the remainder when N is divided by 1000?