Question

Using the digits of the number $223355888$, how many nine digit numbers can be formed so that odd digits occupy even positions?

• A. $16$
• B. $36$
• C. $60$
• D. $180$

Answer 1

Answer: (C)

$60$

There are $4$ even positions and $4$ Odd digits are $(3,5repeating)$ in the given number.

$\Rightarrow$ This can be arranged in $=\frac{4!}{2!\times 2!}$ Ways $=6$

$\Rightarrow$ The rest $5$ digit can be arranged in $\frac{5!}{2!\times 3!}$Ways ( $8$ repeating $3$ times , $2$ repeating $2$ times ) $=10$

$\Rightarrow$ Total $=6\times 10=60$

Hence, the answer is $60.$