Question

How many different nine-digit numbers can be formed from the number $223355888$ by rearranging its digits so that the odd digits occupy even positions?

• A. 16
• B. 36
• C. 60
• D. 180

Answer 1

Answer: (C)

$X-X-X-X-X.$ The four digits $3,3,5,5$ can be arranged at (- ) places in $\frac{4!}{2!2!}=6$ways
The five digits $2,2,8,8,8$ can be arranged at $(X)$ places in $\frac{5!}{2!3!}ways=10ways$
Total number of arrangements $=6\times 10=60$
[since, events $A$ and $B$ are independent, therefore
$A\cap B=A\times B]$