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What is the value of this probability expression?

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First let's change it from binomial form so it might be a little easier to talk about.

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Now we can start tackling one term at a time. Let's start on the top with 4 choose 2. That's 4 factorial, over 2 factorial, multiplied by, 4 minus 2 factorial

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Calculating that term, its value is 6, so we can plug that in.

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Now let's move to the bottom and tackle 2 choose 2. That's 2 factorial, over 2 factorial, multiplied by, 2 minus 2 factorial

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Since both zero and one, factorial, are just 1, our value is 1, so we can plug that in.

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Now our final term is 3 choose 2. That's 3 factorial, over 2 factorial, multiplied by, 3 minus 2 factorial

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Which has a value of 3

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With all terms calculated, we can see that our expression's value is 2