You choose three numbers from 1, 2, 3, .., 21. Find the probability that they are in arithmetic progression.
+128475 No. of sets where common difference (cd) = 1 = 19
No. of sets where cd = 2 = 17
No. of sets where cd = 3 = 15
No.of sets where cd = 4 = 13
No. of sets where cd = 5 = 11
No. of sets where cd = 6 = 9
No. of sets where cd = 7 = 7
No. of sets where cd = 8 = 5
No. of sets where cd = 9 = 3
No. of sets where cd = 10 = 1
Total sets = = (n sets)^2 = (10)^2 = 100
C (21,3) = 1330
Probability = 100 / 1330 = 10 / 133
