Question

A seven-digit number is formed using digit $3,3,4,4,4,5,5.$ The probability, that number so formed is divisible by $2$, is:

• A. $\frac{6}{7}$
• B. $\frac{4}{7}$
• C. $\frac{3}{7}$
• D. $\frac{1}{7}$

Answer 1

The correct option is C $\frac{3}{7}$

Number of ways in which the seven digited number formed is
$n\left(s\right)=\frac{7!}{2!3!2!}$
Number of ways in which the seven digited number is divisible by $2$ is
$n\left(E\right)=\frac{6!}{2!2!2!}$
Hence required probability is
$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{6!}{7!}\times \frac{2!3!2!}{2!2!2!}=\frac{3}{7}$