Question

Three fair and unbiased dice and rolled at a time. The probability that the numbers shown are totally different is.

• A. $\frac{5}{9}$
• B. $\frac{27}{216}$
• C. $\frac{4}{9}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{5}{9}$

Number of elements in sample space =$n\left(s\right)=6^3$ = 216 ways
n(E) =Available 6 different numbers or 3 places in $6_{P_3}$ = 120 ways
Hence $P\left(E\right)=\frac{120}{216}=\frac{5}{9}$