Question

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

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

Answer 1

Answer: (C)

Digits $=3,3,4,4,4,5,5$
Total 7 digit numbers $=\frac{7!}{2!2!3!}$
Number of 7 digit number divisible by 2 $\Rightarrow$ last digit $=4$

Now $7$ digit numbers which are divisible by $2$
$=\frac{6!}{2!2!2!}$
Required probability $=\frac{\frac{6!}{2!2!2!}}{\frac{7!}{3!2!2!}}=\frac{3}{7}$