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?

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.

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