Question

Three dice are rolled and told that exactly two of them are showing the same number. The probability of getting a sum $16$ on them is

• A. $\frac{1}{15}$
• B. $\frac{1}{5}$
• C. $\frac{1}{45}$
• D. $\frac{3}{5}$

Answer 1

The correct option is C $\frac{1}{45}$

The total number of outcome possible
$n\left(S\right)={}^3{C}_2\times {}^6{C}_1\times 5=90$
Outcomes to get a sum of $16$ are
$6,6,4\text{or}5,5,6$
Total favourable outcomes,
$n\left(E\right)=2\times {}^3{C}_2=6$
$P\left(E\right)=$$\frac{6}{90}=\frac{1}{15}$