The probability that a randomly chosen 5 digit number is made from exactly two digits is
150104
121104
134104
The number of five digit numbers when the repition allowed is 9·104 The number of five digit numbers with the speicified two digits There are two cases. Case (i): Suppose that the number has no zero. select two digits from 9 and arrange them in five blnaks with repetion. this can be done in C(9,2)(25-2) Case (ii) Suppose that the number has zero Select one digit from 9, this can be done in 9 ways and fix it in the first place remaining 4 digits can be filled with any of these two digits this can be done in 9·(24-1) ( the number formed by only one digit subtracted from te bunch) The required probability is C(9,2)(25-2)+C(9,1)(24-1)9·104=135104