Combinatorics: Even 3-Digit Numbers from 1-7 with Restrictions

[Dell]

given the numbers 1 2 3 4 5 6 7, how many even 3 digit numbers can be made from these 7 digits
a) if each number can only be used once
b) if each number can be rused


for b) what i did was:
for the first digit i have 7 options, for the second still 7, since i can reuse, and for the 3rd only 3 since the last digit needs to be even

7*7*3=147

but for a) i am stuck, for the first i have 7 options, for the second i have 6 since i have used one already, but how many do i have for the final digit, i would think 3, but what if the 1st 2 were also even, then i only have 1 even left? the correct answer is 90 but i cannnot get it

 

[lanedance]

try counting from the even digit first... ie pick the smallest digit first then so on...

 

[Dell]

nice, thanks

3*5*6