Question

Five persons $A,B,C,D\&E$ are in queue of a shop. The probability that$A\&E$ are always together, is

• A. $\frac{1}{4}$
• B. $\frac{2}{3}$
• C. $\frac{2}{5}$
• D. $\frac{3}{5}$

Answer 1

The correct option is C

$\frac{2}{5}$

Finding the probability:

Given 5 person are in queue of a shop $A,B,C,D\&E$

$A\&E$ itself can arrange in two ways therefore number of arrangement for $A\&E$is $2!$

The probability that$A\&E$ are always together $\frac{2!.4!}{5!}$

therefore,

$\begin{array}{rcl}& & \frac{2!.4!}{5!}\\ & =& \frac{2\times 4!}{5\times 4!}\\ & =& \frac{2}{5}\end{array}$

Therefore the probability that $A\&E$ are always together is $\frac{2}{5}$

Hence, option C is correct.