Two numbers a and b are chosen simultaneously from the set of integers 1 ,   2 ,   3 , … ,   39 , then the probability that the equation 7 a - 9 b = 0 is satisfied is

Step-by-step solution

Total cases = Selection of two numbers simultaneously = C 39 2 = 39 × 19 = 741 For favorable cases a = 9 b 7 ⇒ b must be a multiple of 7 and a ≤ 39 ⇒ b = 7 , a = 9 b = 14 , a = 18 b = 21 , a = 27 b = 28 , a = 36 Only 4 possible cases Hence, the required probability = 4 741