Question

A seven-digit number is formed using the 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

$\frac{3}{7}$

Explanation for the correct option:

Step1. Total $7$ digit numbers $n\left(S\right)=\frac{7!}{[2!3!2!]}$

Given Digits $=3,3,4,4,4,5,5$

Number of $7$digit number which are divisible by 2

$\Rightarrow$last digit $=4$

Step 2. $7$ digit numbers divisible by 2, $n\left(E\right)=\frac{6!}{[2!2!2!]}$

Therefore, Required probability $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\left[\frac{6!}{7!}\right]\times \left[\frac{\left(2!3!2!\right)}{\left(2!2!2!\right)}\right]=\frac{\mathbf{3}\mathbf{}}{\mathbf{7}}$

Hence, Option ‘C’ is Correct.