# What Is The Number Of Even Numbers Greater Than 100 That Can Be Formed With 0 1 2 3?

Because we want even numbers, the 1s digit must be 0 or 2.
When the 1s digit is 0, we can freely choose the remaining digits. There are 6 permutations of 3 digits taken 2 at a time (to make a 3-digit number ending in 0), and 6 permutations of 3 digits taken 3 at a time (to make a 4-digit number ending in 0). Thus, there are 12 ways to make a 3- or 4-digit number ending in 0 from the given digits.

When the 1s digit is 2, we need to choose the 100s digit of the 3-digit numbers from the set {1, 3}. The 10s digit can be either of the remaining two digits, for a total of 2*2 = 4 ways to make a 3-digit number ending in 2.

The same restriction applies for the 4-digit numbers ending in 2: The 1000s digit must be from the set {1, 3}, and the remaining digits are free choice. Again, there are 2*2*1 = 4 ways to choose those.

We have a total of 12 numbers ending in 0, and 8 numbers ending in 2, for a total of 20 even numbers greater than 100 made from digits {0, 1, 2, 3}.

The entire list is
120, 130, 210, 230, 310, 320, 1230, 1320, 2130, 2310, 3120, 3210,
102, 132, 302, 312, 1032, 1302, 3012, 3102.
thanked the writer.