Question 16550 – TIFR PHD 2022

Initially, N white beads are arranged in a circle. A number k is chosen uniformly at random from {1, . . . ,N − 1}. Then a set of k beads is chosen uniformly from the white beads, and these k beads are coloured black. The position of the beads remains unchanged. What is the probability that the black beads occur sequentially in the circle, i.e., at most two black beads have white beads next to them?

Correct Answer: C