The probability that a randomly chosen 5 - digit number is made from exactly two digits is :

Step-by-step solution

Total number of five-digit numbers are 9 10 4 . Case I : Choosing two non-zero digits i.e. in C 2 9 ways. So, number of five-digit numbers containing both digits = 2 5 - 2 . Case II : Choose one non-zero and one zero as digit i.e. in C 1 9 ways. So, number of five-digit numbers containing one non-zero and one zero both = 2 4 - 1 . So, favourable number of ways = C 2 9 2 5 - 2 + C 1 9 2 4 - 1 = 36 30 + 9 15 = 1080 + 135 = 1215 Thus, required probability = 1215 9 × 10 4 = 135 10 4 .