Question

The number of ways in which we can get a sum of the score of $11$ by tossing three dices is?

• A. $18$
• B. $27$
• C. $45$
• D. $56$

Answer 1

The correct option is B

$27$

The explanation for the correct answer.

Find the number of ways to get the sum $11$:

Given: Three dices are rolled.

Ways we get sum $11$are

$$\begin{gathered} \left(1,6,4\right)=3!=6 \\ \left(3,3,5\right)=\frac{3!}{2!}=3\mathbf{}\left(Wayswhentermsarelike=\frac{n!}{k!(karethenumberofliketerms)}\right) \\ \left(2,6,3\right)=3!=6 \\ \left(2,5,4\right)=3!=6 \\ (1,5,5)=\frac{3!}{2!}=3 \\ \left(3,4,4\right)=\frac{3!}{2!}=3 \end{gathered}$$

Therefore the number of ways $=6+3+6+6+3+3=27$

Hence option $\left(B\right)$ is the correct answer.