Three distinct numbers are selected randomly from the set 1,2,3, , 40 . If the probability, that the selected numbers are in an increasing G.P. is m n , gcd (m, n)=1 , then m+n is equal to _____.

Step-by-step solution

1 a ar ar ^2 40 (If r N ) If r=2 1 a 2 a 4 a 40 a 1, ., 10 ________ (10 GP) If r=3 1 a 3 a 9 a 40 a 1,2,3,4 ________ ________ (4 GP) If r =4 1 a 4 a 16 a 40 a 1,2 ________ ________ (2 GP) If r=5 1 a 5 a 25 a 40 a 1 ________ ________ (1 GP) If r=6 1 a 6 a 36 a 40 a 1 ________ ________ (1 GP) ( P = 18 9880 = 9 4940 ) as per NTA for r N m + n =4949 If r ~N (also possible) r = 3 2 ar ^2= 9 a 4 ; a =4 k . array l (4,6,9) (8,12,18) (12,18,27) (16,24,36) array 4 GP aligned & array l r = 5 2 ar ^2= 25 a 4 ; a =4 k (4,10,25