Question

The number of nine digit number that can be formed using the digits 2,2, 3,3, 5,5, 8,8, 8, so that the odd digits occupy even positions is

• A. 180
• B. 7560
• C. 60
• D. 16

Answer 1

The correct option is C 60

4 odd digits (3,3,5,5) occupy 4 even places in $\frac{4!}{2!2!}=6$ ways
5 even digits (2, 2 8,8,8) occupy 5 odd places in $\frac{5!}{2!3!}=6$ ways
Total nine digit number so that odd digits occupy even place $6\times 10=60$ ways