Three dice are thrown. The probability of getting a sum of numbers which is a perfect cube, is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{7}{72}\)
Three dice give sums from 3 to 18, and the only perfect cube in that range is 8 (1 is too small, 27 too large). So count the ways of getting a sum of 8 among the \(6^3=216\) equally likely outcomes.
Ways of getting a sum of 8: 21
1, 1, 6 in any order: 3 ways
1, 2, 5 in any order: 6 ways
1, 3, 4 in any order: 6 ways
2, 2, 4 in any order: 3 ways
2, 3, 3 in any order: 3 ways
Probability \(\displaystyle=\frac{21}{216}=\frac{7}{72}\)