Question

Out of 9 consecutive integers, three are selected at random. The probability that their sum is divisible by 3 is

• A. $\frac{5}{14}$
• B. $\frac{2}{14}$
• C. $\frac{3}{14}$
• D. $\frac{9}{14}$

Answer 1

The correct option is A $\frac{5}{14}$

x, x + 1, x + 2,..., x + 8 be any 9 consecutive integers.
$n\left(E\right){=}^3{C}_1{\bullet }^3{C}_3+3^3=30$
$n\left(S\right){=}^9{C}_3$
$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{5}{14}$.