What is the probability that in a randomly chosen group of r people at least…

GATE · 2008 · IT· Modified — slightly modified from the official paper; see the solution

1. A.

   1 − 365·364·…·(365−r+1) / 365^r

2. B.

   365·364·…·(365−r+1) / 365^r + C(r,2)·365·364·363·…·(364−(r−2)+1) / 364^(r−2)

3. C.

   1 − Σ_(k=0)^(⌊r/2⌋) [r!/(2^k k!(r−2k)!)]·(365)_(r−k)/365^r

4. D.

   365·364·…·(365−r+1) / 365^r

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