Question

1. %) Even integers with non repeating digits. Even integers are integers ending in 0, 2, 4, 6, 8. It is easy to see that for 2 digits integers, the number of 2 digits even integers is 45 (i.e. from 10 to 99, 10, 12, 14, …, 96, 98 are the 2 digits even integers); for 3 digits integers, the number of 3 digits even integers is 450 (from 100 to 999, 100, 102, 104, .. , till 994, 996, 998), and so on.

Now consider even integers with non-repeating digits. Calculate the number of even integers where digits can not be repeated

1. (3%) For 2 digits (how many even integers are among 10, 12, .., 96, 98 with non-repeating digits? This means 22, 444, 66, and 88 are not counted. Anything else)?
2. (5%) For 3 digits (how many even integers are among 100, 102, .., 996, 998 with non-repeating digits? Note this means 112, 202, 222, etc. are not included, but 102, 104 etc. are included.)
3. (7%) For 4 digits.

Answer 1

Answer: ---- Date: ----10/7/2019