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 :
Correct Option: , 3
Solution:
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 $=\frac{\frac{6 !}{2 ! 2 ! 2 !}}{\frac{7 !}{3 ! 2 ! 2 !}}=\frac{3}{7}$