# I am onion!

**Discrete Mathematics**Level 3

\(\bullet\) The number of \(\color{Purple}{Purple}\) onions can be any non-negative integer.

\(\bullet\) The number of \(\color{Green}{Green}\) onions is a multiple of 2.

\(\bullet\) The number of \(\color{Red}{Red}\) onions is a multiple of 3.

\(\bullet\) The number of \(\color{Blue}{Blue}\) onions is a multiple of 5.

If Cody has 23 onions, how many different distributions of colors can there be?

**Details and Assumptions**: Cody can't have a negative number of onions, but he may have 0 onions of a certain type(s).