The probability of ranining on any given day is 0.3. What is the probability that it rains on exactly three days out of six?

Let a day of rain be R.

Let a day of no rain be N.

What is the probability of getting R R R N N N?

It is 0.3x 0.3 x 0.3 x 0.7 x 0.7 x 0.7= 0.009261

But that is just 1 combination. How many combinations are there? Think of RRRNNN like a 6-letter word with 3 and 3 repeats. Thus use the formula 6!/3! x 3! and you get 20 possible combinations. So finally, 20 x 0.009261=0.18522

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