You buy a package of 12 tulip bulbs labeled as mixed colors

You buy a package of 12 tulip bulbs labeled as “mixed colors”. The supplier of these bulbs explains that what they mean by that is that any given tulip bulb has a 40% probability of producing red flowers, a 30% probability of white, a 20% probability of yellow, and a 10% probability of orange. But the 12 bulbs in each package are selected randomly, so the supplier was making no conscious attempt to have an even mix. You just have to plant the bulbs and take whatever you get. Your ideal would be to end up with 4 red tulip plants, 4 white plants, 2 yellow plants, and 2 orange. What is the probability of getting your ideal combination?

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