Question

Three dice are rolled. what is the probability of getting the sum as 13

Answer 1

When three dices are rolled.

Total number of outcomes = $6^3$ = 216

Sum of 13 can be achieved in the following ways:

From the digits 6,4,3

So, there are 3! ways = $3 \times 2$ = 6

From the digits 6,2,5

So, there are 3! ways = $3 \times 2$ = 6

From the digits 5,4,4

So, there are $\frac{3!}{2!}$ ways = 3

From the digits 6,6,1

So, there are $\frac{3!}{2!}$ ways = 3

From the digits 3,5,5

So, there are $\frac{3!}{2!}$ ways = 3

So, total numbers whose sum is 13= $(6+6+3+3+3) = 21$

So, Probability = $\frac{21}{216}$.

Therefore, the probability of getting sum as 21 on rolling three dice =   $\frac{21}{216}$.

Answer 2

Answer:

21/216

Step-by-step explanation:

When three dices are rolled.

Total number of outcomes =  = 216

Sum of 13 can be achieved in the following ways:

From the digits 6,4,3

So, there are 3! ways =  = 6

From the digits 6,2,5

So, there are 3! ways =  = 6

From the digits 5,4,4

So, there are  ways = 3

From the digits 6,6,1

So, there are  ways = 3

From the digits 3,5,5

So, there are  ways = 3

So, total numbers whose sum is 13=  

So, Probability = .21/216

Therefore, the probability of getting sum as 21 on rolling three dice =  21/216.

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