How many four digit whole numbers are there that the thousand digit is odd the hundred digit is even and all four digit are different?

Answer 1

Number of ways that the thousand digit can be odd = 5 (1, 3, 5, 7, or 9)

Number of ways that the hundred digit can be even = 5 (0, 2, 4, 6, or 8)

These two digits are always different. Total number of possible pairs = 5 x 5 = 25.

For each pair, the tens digit can be any one of 8 digits (it can't be the same as

either the thousands or the hundreds) = 8 possibilities for the tens digit.

For each of those, the units digit can be any one of 7 digits (it can't be the same as

the thousands, the hundreds, or the tens) = 7 possibilities for the units digit.

Total number of different numbers that can be written according to these rules =

25 x 8 x 7 = 1,400