Question

A bag contains $20$ cards $10$ of these cards have letter ${}^{\prime }{E}^{\prime }$ $5$ have letter ${}^{\prime }{I}^{\prime }$ and other $5$ have letter ${}^{\prime }{A}^{\prime }$ printed on them, if five cards are drawn one by one and are kept in same order aside then probability of making the words $AIEEE$ is

• A. $5/36$
• B. $25/2584$
• C. $36/2584$
• D. $26/37$

Answer 1

The correct option is B $25/2584$

Total$=20$

$10=E$

$5=I$

$5=A$

Now,

$AIEEE$

$\begin{array}{c}\frac{5}{20}\times \frac{5}{19}\times \frac{10}{18}\times \frac{9}{17}\times \frac{8}{16}\\ =\frac{25}{2584}\end{array}$

Hence, the option $B$ is the correct answer.