Question

4 five-rupee coins, 3 two-rupee coins and 2 one-rupee coins are stacked together in a column at random. The probability that the coins of the same denomination are consecutive is

• A. $\frac{13}{9!}$
• B. $\frac{1}{210}$
• C. $\frac{1}{35}$
• D. none of these

Answer 1

The correct option is B $\frac{1}{210}$

$n\left(S\right)=\frac{9!}{4!3!2!}$ and $n\left(E\right)=3!$

$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{3!}{\frac{9!}{4!3!2!}}=\frac{3!4!3!2!}{9!}$
$=\frac{\mathrm{6.6.2}}{\mathrm{9.8.7.6.5}}=\frac{1}{210}$