Random selection

Question

6 numbers are randomly selected between 1 and 100. What is the probability that all are distinct

Answer 1

Assuming that a number once selected can be selected once again and 1 and 100 inclusive ,

Cardinality of sample space = 100 * 100 * 100 * 100 * 100 * 100 * 100 = (100)⁶ [ Since repetition is allowed so we have 100 choices in every trial]

But favourable outcome here is to have 6 distinct numbers .

So number of ways for 1st trial (choices) = 100

  So once a number is selected , it will not be selected once again , so choice for 2nd trial = 99

  Similarly , for 3rd trial   =   98

  So no of favorable outcomes for 6 trials = 100 * 99 * 98 * 97 * 96 * 95

 Hence P(E)   =   n(E)/ n(S)

                     = (100 * 99 * 98 * 97 * 96 * 95) / (100)⁶