Question as follows A bag contains 50 tickets numbered 1,2,3,....,50 of which five are drawn at random and arranged in ascending order of the number appearing on the tickets ( x1 < x2 < x3 < x4 < x5 ). Find the probability that x3 = 30.
Total number of elementary events =50C5 Given,third ticket =30
=> first and second should come from tickets numbered 1 to 29 =29C2 ways and remaining two in 20C2 ways.
Therfore,favourable number of events = 29C2×20C2
Hence,required probability = (29C2×20C2)/50C5 =551 / 15134
Answer given is 551/15134 but in the solution they have taken the case where x2 will be less than x1. Is my assumption correct? if it is not then what could be the correct answer.