If four caps are picked at random, what is the probability that none is green?

Total number of caps = 12
Total number of result = n(S) = ¹²C₄ = 495
Out of 5 caps, number of ways to not pick a green cap = n(E₁) = ⁵C₀ = 1
and out of 7 caps, number of ways to pic 4 caps = n(E) = ⁷C₄ = 35
∴ Required probability = (1 x 35)/495 = 7/99