Question

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

• A. 16
• B. 36
• C. 60
• D. 180

Answer 1

Answer: (C)

60

Answer 2

There are 4 even place and 4 odd digits. So their arrangement is = $\frac{\begin{matrix} 4 \end{matrix}}{\begin{matrix} 2 \end{matrix}\begin{matrix} 2 \end{matrix}}$ (33 55)

and arrangement of seven digit at 5 place is

= $\frac{\begin{matrix} 5 \end{matrix}}{\begin{matrix} 2 \end{matrix}\begin{matrix} 3 \end{matrix}}$ (22, 888)

Total number = $\frac{\begin{matrix} 4 \end{matrix}}{\begin{matrix} 2 \end{matrix}\begin{matrix} 2 \end{matrix}}$ × $\frac{\begin{matrix} 5 \end{matrix}}{\begin{matrix} 2 \end{matrix}\begin{matrix} 3 \end{matrix}}$