=+17. Consider a family of subsets F of a set S with the property that each A ∈ F has exactly d elements. The family F is said to be 2-colorable if we can assign one of two colors, say black and white, to each element of S in such a manner that each A ∈ F possesses at least one element of each color. Prove that F is 2-colorable if it contains fewer than 2d−1 subsets [1]. (Hints: Randomly color each element of S with one of the two equally likely colors black and white. Let CA be the event that all elements of A ∈ F receive the same color. Show that ∪ACA has probability strictly less than 1.)