A hacker discovers that the first two digits of a person's ATM PIN are from the numbers 3 to 8, and the fourth digit is 0 or 9. How many attempts will the hacker have to make to find out the PIN?

Explanation

∵ Number of digits in an ATM pin = 4 <table> <tr> <th>6</th> <th>6</th> <th>10</th> <th>2</th> </tr> </table> ∴ Number of digits that can appear in the first and second positions = 6 Total digits can appear in the third position = 10 No. of Digit can appear in the fourth position = 2(0 or 9) ∴ The number of attempts made by the hacker to obtain the PIN = $6 \times 6 \times 10 \times 2$ = 720