In a draw of lottery, tickets numbered 1 to 50 were thoroughly shuffled and put in an urn. Then three tickets were drawn randomly from the urn, what is the probability that there is at least one ticket with one digit number in the drawn tickets?

Number of ways of drawing 3 tickets out of 50 = ⁵⁰C₃ Number of two-digit tickets = 50 - 9 = 41 (since number of one-digit tickets, i.e. tickets marked 1 to 9 = 9)
Number of ways of drawing 3 tickets out of 41 = ⁴¹C₃ Therefore, probability of getting two-digit numbered ticket = (⁴¹C₃)/(⁵⁰C₃) Probability of getting at least 1 one-digit numbered ticket = 1 - probability of getting two-digit numbered ticket So, required probability = 1 - (⁴¹C₃)/(⁵⁰C₃)