Of three digit positive integers whose three digits are all different and non zero, how many are odd integers greater than 700
1)84
2)91
3)100
4)105
5)243
Case 1: Hundreds digit is 7 or 9
Number of options for the hundreds digit = 2. (7 or 9)
Number of options for the units digit = 4. (Any odd digit but the one in the hundreds place)
Number of options for the tens digit = 7. (Any digit 1-9 but the two already used)
To combine these options, we multiply:
2*4*7 = 56.
Case 2: Hundreds digit is 8
Number of options for the hundreds digit = 1. (Must be 8)
Number of options for the units digit = 5. (Any of the 5 odd digits)
Number of options for the tens digit = 7. (Any digit 1-9 but the two already used)
To combine these options, we multiply:
1*5*7 = 35.
Total options = 56+35 = 91.
The correct answer is
B.
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