I am onion!

Probability Level 3

Cody has 4 types of onions:

  • The number of purple\color{#69047E}\text{purple} onions can be any non-negative integer.
  • The number of green\color{#20A900}\text{green} onions is a multiple of 2.
  • The number of red\color{#D61F06}\text{red} onions is a multiple of 3.
  • The number of blue\color{#3D99F6}\text{blue} onions is a multiple of 5.

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

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