# Moderate Probability Solved QuestionAptitude Discussion

 Q. If five dice are thrown simultaneously, what is the probability of getting the sum as seven?
 ✔ A. $\dfrac{15}{6^5}$ ✖ B. $\dfrac{11}{6^5}$ ✖ C. $\dfrac{10}{6^5}$ ✖ D. $\dfrac{5}{6^5}$

Solution:
Option(A) is correct

The following are two cases when the sum will be 7:

$7=1+1+1+1+3 \Rightarrow ^5C_1$ ways = 5

$7=1+1+1+2+2 \Rightarrow ^5C_2$ ways = 10

Total number of possible ways of throwing five dice $=6^5$

The required probability

$=\dfrac{15}{6^5}$

Edit: Based on Poonam Pipaliya's comment, solution has been modified.

## (4) Comment(s)

Sudhanva Dixit
()

How is $1+1+1+2+2=^5C_2$ ways?

Aarti
()

It is not mathematically equal, it equals the number of ways three, 1's and two, 2's can be obtained from five dice.

Poonam Pipaliya
()

in second line there should be $1+1+1+2+2=7$

Deepak
()

Yes Poonam, you are right, corrected the solution.