A sequence of two different digits is randomly chosen from t

A sequence of two different digits is randomly chosen from the digits 0-4; the first digit is larger than the second. Describe the sample space S of the experiment. (Select all that apply.)

Solution

The first number can be choosen from 0-4 but it cannot be 0 because it is given that the second digit is less the first digit and there is no number less than 0 in 0-4. Thus there are 4 ways to choose first digit. If the first digit is n then there are n ways to select the second digit in 0-4 from permutation.

Thus if first digit is 1 then there is 1 way to select second digit and the only possible value is 0 (1,0). Similarly if first digit is 2 then there are 2 ways to select second digit and the possible values are 0,1 (2,1),(2,0). If first digit is 3 then there are 3 ways to select second digit and the possible values are 0,1,2 (3,0),(3,1),(3,2). If first digit is 3 then there are 3 ways to select second digit and the possible values are 0,1,2,3 (4,0),(4,1),(4,2),(4,3).