I believe that the problem intends to ask the following:
How many even numbers, larger than 400, with 3 digits, can be formed using the digits 1,2,3,4,5,6,7,8, if no digit can be repeated?
a.102
b.620
c.640
d.2048
e.2520
Case 1: units digit = 4, 6, or 8
Number of options for the units digit = 3. (4, 6 or 8.)
Number of options for the hundreds digit = 4. (Of 4, 5, 6, 7, and 8, any digit but the one chosen to be the units digit.)
Number of options for the tens digit = 6. (Any of the 6 remaining digits.)
To combine these options, we multiply:
4*3*6 = 72.
Case 2: units digit = 2
Number of options for the units digit = 1. (Must be 2.)
Number of options for the hundreds digit = 5. (4, 5, 6, 7, or 8.)
Number of options for the tens digit = 6. (Any of the 6 remaining digits.)
To combine these options, we multiply:
1*5*6 = 30.
Total options = 72+30 = 102.
The correct answer is
A.
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