GATE 2014 CS (CS1) – Question 58
Four fair six-sided dice are rolled. Probability that the sum is 22 equals X/1296. Find X.
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Correct answer: 10 to 10
Explanation
The maximum sum is24. Let each deficit from6 be nonnegative; the deficits must sum to2. Stars and bars gives C(2+4−1,4−1)=C(5,3)=10, with no upper-bound restriction active. Among6⁴=1296 equally likely outcomes, the numerator is **X=10**.