Exercise 5.

Consider five digit numbers \(\alpha = a_1a_2a_3a_4a_5\text{,}\) with each digit from the set \(\{1,2,3,4\}\text{.}\)

  1. How many such numbers are there?

  2. How many such numbers are there for which the sum of the digits is even?

  3. How many such numbers contain more even digits than odd digits?

in-context