Solution. a) The first digit can be chosen in nine ways

a) The first digit can be chosen in nine ways.

The second digit can be chosen in eight ways.

The third digit can be chosen in seven ways.

Total number of three-digit numbers that are all different

b) If the three digits are all the same then there are nine possible three-digit numbers, since the only possibilities are 111, 222, 333, 444, 555, 666, 777, 888 and 999.

c) If the number is greater than 600 then there are only four choices for the first digit: 6, 7, 8 or 9.

The second and third digits can each be chosen in nine ways.

Total number of three-digit numbers

d) In this case we start with the last digit as this is the one with the restriction.

The last digit can be chosen in four ways.

The other two digits can be chosen in eight ways and seven ways respectively.

Total number of three-digit numbers that are all different