BTGmoderatorLU wrote:How many odd three-digit integers greater than 800 are there such that all their digits are different?
A. 40
B. 56
C. 72
D. 81
E. 104
Case 1: Hundreds digit = 8
Number of options for the units digit = 5. (Any of the 5 odd digits.)
Number of options for the tens digit = 8. (Of the 10 digits, any but the two already used.)
To combine the options above, we multiply:
5*8 = 40.
Case 1: Hundreds digit = 9
Number of options for the units digit = 4. (Of the 5 odd digits, any but 9.)
Number of options for the tens digit = 8. (Of the 10 digits, any but the two already used.)
To combine the options above, we multiply:
4*8 = 32.
Total number of viable integers = Case 1 + Case 2 = 40 + 32 = 72.
The correct answer is
C.
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