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Q9 (CAPF/2012) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Quantitative aptitude topics Answer Verified

Three dice, whose all six faces arc- marked ‘1’ to ‘6’, are thrown. The number of ways of getting a sum of 16 is

Result
Your answer: —  ·  Correct: C
Explanation

To find the number of ways to obtain a sum of 16 with three six-sided dice, we identify the combinations of three numbers between 1 and 6 that sum to 16. The possible sets of numbers are {6, 6, 4} and {6, 5, 5}. Since the dice are distinct, we must count the permutations of these sets. For the set {6, 6, 4}, there are 3 permutations: (6, 6, 4), (6, 4, 6), and (4, 6, 6). For the set {6, 5, 5}, there are also 3 permutations: (6, 5, 5), (5, 6, 5), and (5, 5, 6). Adding these together, we get 3 + 3 = 6 total ways. This can also be verified by considering the total outcomes (216) and subtracting outcomes for sums of 17 (3 ways) and 18 (1 way) from the total ways to get a sum of 16 or more.

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