Question

I did a question that asked how many 3digit even numbers can be made using the digits 1,2,3,4,5,6,7 if no digit is repeated?
then the answer when I checked was fpc=3X5X4=60
But for an even number if only the last digit is even then the number will be even as it is
So why it can't be fpc=7X6X3. ?

Answer 1

Actually the answer is wrong and your try is also incorrect
the correct answer is 3X6X5 = 90
No Digit should be repeated, so in the asnwer the logic is
3... because the number of even numbers is even so 3 possibilities for the one's place,
6... because the number of digits left with us for the ten's once we have used one in the one's place.
5... because the number of digits left with us for the hundred's once we have used one in the one's place, and one in the ten's place.
always start from what matters the most, as here even number matters the most so we start from the one's place

your answer is incorrect because you started from the hundred's place and hence you had all the seven possibilities for it, and 6 for the one's place but there will be one case there in which we will use up 2 of the even numbers already in the hunderd's and one's place and we will be left with only one even number and hence the solution would not be obeyed.