Question

In a box, there are $8$ alphabets cards with the letters: $S,S,A,A,A,H,H,H$. Find the probability that the word $ASH$ will form if three cards are drawn simultaneously.

• A. $\frac{9}{28}$
• B. $\frac{19}{28}$
• C. $\frac{9}{14}$
• D. $\frac{5}{14}$

Answer 1

The correct option is A $\frac{9}{28}$

Given, 8 alphabets cards with letters: $S,S,A,A,A,H,H,H$ are present.
Three cards are drawn simultaneously,
Total no. of outcomes when $3$ cards are drawn, $N=\frac{{}^8{C}_3}{(2!\times 3!\times 3!)}$ (since same letters exist in the set)
$\Rightarrow N=56$
The no. of outcomes to form word $ASH$, $n\left(X\right)=2C_1\times 3C_1\times 3C_1=18$
$\therefore$ The required probability$=\frac{n\left(X\right)}{N}=\frac{18}{56}=\frac{9}{28}$