The number of even numbers greater than 100 that can be formed by the digits 0, 1, 2, 3 (no digit being repeated) is

The numbers are of three or four digits.To find the number of even numbers of three digits—The unit’s place must be filled by 0 or 2.∴ The number of even numbers of three digits (having or not having 0 in hundred’s place) =2P1×3P2.But the number of even numbers of three digits having 0 in hundred’s place =2P1 (∵ unit’s place is naturally filled by 2 and ten’s place by one of 1 and 3).∴ The number of even numbers of three digits=2P1×3P2−2P1            (1)Similarly, the number of even numbers of four digits=2P1×3P3−2P2            (2)Adding (1) and (2), we get the number of even numbers greater than 100= 2P1×3P2−2P1+ 2P1×3P3−2P2=2×3×2−2+2×3×2×1−2×1=20