A dice is rolled three times and sum of three numbers appearing

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A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was four is

1. 2/5
2. 1/5
3. 1/6
4. None of these

Correct Option: D

Total number of favourable outcomes n(S) = 6³ = 216
Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6), (5, 4, 6), ( 6, 5, 4), (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5),(6, 6, 3), (6, 3, 6), (3, 6, 6)
Now, outcomes on which first roll was a four, n(E) = (4, 5, 6),(4, 6, 5)
∴ P(E) = n(E)/n(S) = 2/216 =1/108