Is that the whole question?
Answer:
7/27 ≈ 25.9%
Step-by-step explanation:
"At most one" means either exactly 0 or exactly 1.
P(at most 1) = P(0) + P(1)
Using binomial probability:
P(r) = nCr pʳ qⁿ⁻ʳ
P(0) = ₃C₀ (⅔)⁰ (⅓)³⁻⁰ = 1/27
P(1) = ₃C₁ (⅔)¹ (⅓)³⁻¹ = 2/9
So the probability that it rains on at most one day is:
P(at most 1) = 1/27 + 2/9
P(at most 1) = 7/27
P(at most 1) ≈ 0.259
Just multiply all of your variations together and you get 144 regardless of whether you only use one item from each category or not your answer will come to be 144 simply because that is how many variations can be made.