Number of different nine digit numbers, that can be formed from the digits in the number 223355888 by…
Number of different nine digit numbers, that can be formed from the digits in the number 223355888 by rearranging its digits, so that the odd digits occupy even positions, is
16
40
60
180
Solution
Since $3,3,5$, 5, i.e., odd digits occupy even positions and $2,2,8,8,8$ occupy remaining 5 odd places.
$\begin{aligned}
\therefore \quad \text { Required number of ways } & =\frac{4!}{2!2!} \cdot \frac{5!}{2!3!} \\
& =6 \times 10=60
\end{aligned}$