Question

If the letters of the word $ASHOKA$ are written down at randomly, then the chance that all $A^{\prime }s$ are consecutive is :

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{1}{3}$

Number of ways in which all the words from the word $ASHOKA$ can be written $=\frac{6!}{2}$
The number of ways in which all the words from the word $ASHOKA$ can be written with all the $A^{\prime }s$ together
$=5!$

Required probability $=\frac{5!}{\frac{6!}{2}}=\frac{1}{3}$