Three dice are thrown simultaneously. probability of obtaining a total of 17 or 18

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14.Probability

easy

Three dice are thrown simultaneously. What is the probability of obtaining a total of $17$ or $18$

A

$\frac{1}{9}$

B

$\frac{1}{{72}}$

C

$\frac{1}{{54}}$

D

None of these

Solution

(c) Three dice can be thrown in $6 \times 6 \times 6 = 216$ ways.

A total $17$ can be obtained as $(5,\,6,\,6)$,$(6,\,5,\,6),$ $(6,\,6,\,5)$.

A total $18$ can be obtained as $(6,\,6,\,6)$.

Hence the required probability $ = \frac{4}{{216}} = \frac{1}{{54}}.$

Standard 11

Mathematics

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