Question

Find the probability that the 3N’s come consecutive in the arrangement of the letters of the word “CONSTANTINOPLE”.

• A. $\frac{3}{91}$
• B. $\frac{2}{91}$
• C. $\frac{4}{91}$
• D. $\frac{2}{91}$

Answer 1

The correct option is A $\frac{3}{91}$

The total number of arrangement of the letters of the word “CONSTANTINOPLE” is $\frac{\left(14\right)!}{3!2!2!}$ Since 3 N’s are consecutive, then considering all the 3 N’s as single letter, the total number of arrangements is $\frac{\left(12\right)!}{2!2!}$
Therefore, required probability is
$\frac{\frac{\left(12\right)!}{2!2!}}{\frac{\left(14\right)!}{3!2!2!}}=\frac{3!}{14\times 13}=\frac{3}{91}$