NandishSS wrote:How many even 3 digit integers greater than 700 with distinct non zero digits are there ?
A. 729
B. 243
C. 108
D. 88
E. 77
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. (2, 4, 6, or 8)
Number of options for the tens digit = 7. (Of the 9 remaining nonzero digits, any but the 2 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 = 3. (2, 4, or 6)
Number of options for the tens digit = 7. (Of the 9 remaining nonzero digits, any but the 2 already used)
To combine these options, we multiply:
1*3*7 = 21.
Total ways = Case 1 + Case 2 = 56+21 = 77.
The correct answer is
E.
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