Question

How many $9$digit numbers can be formed by using the digits $1,1,2,2,2,2,3,4,4$such that odd numbers occur at even places?

• A. $160$
• B. $175$
• C. $180$
• D. $220$

Answer 1

The correct option is C

$180$

To find the total numbers:

Odd numbers$=1,1,3\left(3\right)$ and even numbers$=2,2,2,2,4,4\left(6\right)$

Even places $=4$

Odd numbers $=3$

Even numbers $=6$

Therefore the total numbers $={}^{4}C_3\times \frac{3!}{2!}\times \frac{6!}{4!2!}=4\times 3\times 15=180$

Hence the correct option is C.