Discrete Mathematics
# Complements

*different* digits?

Do not include leading zeros when counting the digits

4 brothers are told to stand in a row for their family portrait. Their heights are:

- Abe: 4'6''
- Ben: 4'
- Clark: 3'6''
- Dan: 3'

There's also a "Happy Birthday Dad!" poster that has to be held by 2 brothers standing next to each other, and in order to hold it straight, those two brothers have to be at most 6'' apart in height.

Mom's a bit crazy and wants to take a bunch of pictures so she has her sons stand in all 4! possible orders (ABCD, DCBA, DCAB, ... etc.) **In how many of the shots can the poster be held evenly?**

Randomly pick a whole number between 10 and 99 (inclusive). Then multiply the digits together. What is the chance that the resulting number is even?

Hint: An odd number times an odd number is an odd number.