Question

Three dice are thrown. the probability of getting a sum that is a perfect square is:

Answer 1

Finding the probability

The total number of outcomes$=6^3=216$

Among all these, we can get perfect squares $4,9,16$

Total ways for an outcome of $4$:

$(1,1,2)$in $3$ possible ways

Total ways =$3$

Total ways for an outcome of $9$:

$(1,2,6)$ in $3!$ possible ways

$(1,3,5)$ in $3!$ possible ways

$(2,3,4)$in $3!$ possible ways

$(3,3,3)$ in $1$ possible way

$(2,2,5)$ in $3$possible ways

$(1,4,4)$ in $3$ possible ways

Total ways =$3!+3!+3!+1+3+3=6+6+6+7=25$

Total ways for an outcome of $16$:

$(4,6,6)$ in $3$ possible ways

$(5,5,6)$ in$3$ possible ways

Total ways =$3+3=6$

Number of favorable outcomes$=3+25+6=34$

Probability of getting a sum of perfect square$=34/216=17/108$