How would you solve this?

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Probability = Number of events we’re interested in / Total number of events

Here, since we have 10 jellybeans and we need to pick 3, without replacement, the total number of events is (we do not care about the order), 10C3 = 120.

Now, we’re interested in the probability that all the 3 picked jellybeans are different. This can be done in 6 ways (since there are 3 distinct flavors, so 3 x 2 x 1 = 6 ways). But we’re not interested in the order.

So, number of such events = Number of ways to pick 1 licorice out of 4 * number of ways to pick 1 marshmallow out of 4 * number of ways to pick 1 orange out of 2

Number of events = 4 * 4 * 2 = 32

So, P(3 different beans) = 32/120 = 4/15

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