Question

The number of ways in which we can get a sum of $11$ by throwing three dice is :

• A. $56$
• B. $8$
• C. $27$
• D. $45$

Answer 1

The correct option is C $27$

Dice is marked with numbers $1,2,3,4,5,6.$

The sum is $11$ when the observations are
$\{1,4,6\},\{1,5,5\},\{2,3,6\},\{2,4,5\}\{3,3,5\},\{3,4,4\}$

The number of ways of getting the observations
$=3!+\frac{3!}{2!}+3!+3!+\frac{3!}{2!}+\frac{3!}{2!}=27\text{ways.}$