Question

$8$ - digit numbers are formed using the digits $1,1,2,2,2,3,4,4$. The number of such numbers in which the odd digits do not occupy odd places, is :

• A. $160$
• B. $120$
• C. $60$
• D. $48$

Answer 1

The correct option is B $120$

Odd = 1, 1, 3 Even = 2, 2, 2, 4, 4.
$(2,2,2,4)+(2,2,4,4)$
$\Rightarrow \frac{4!}{3!}\times \frac{4!}{2!}+\frac{4!}{2!2!}\times \frac{4!}{2!}$
$\Rightarrow 4\times 12+6\times 12$
$\Rightarrow 48+72$
$=120$