A seven digit number is

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 :

  1. $\frac{6}{7}$

  2. $\frac{1}{7}$

  3. $\frac{3}{7}$

  4. $\frac{4}{7}$


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 $=\frac{\frac{6 !}{2 ! 2 ! 2 !}}{\frac{7 !}{3 ! 2 ! 2 !}}=\frac{3}{7}$

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