# 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.

## (5) 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.

PRAKASH SAMANTA
()

${^5C_2}$ ways because-

1+1+1+2+2

1+1+2+1+2

1+2+1+1+2

1+1+2+2+1

1+2+2+1+1

1+2+1+2+1

2+1+1+1+2

2+1+1+2+1

2+1+2+1+1

2+2+1+1+1

Poonam Pipaliya
()

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

Deepak
()

Yes Poonam, you are right, corrected the solution.