Question

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearrangement of the digits so that the odd digits occupy even places?

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

Answer 1

Answer: (A), (C)

The correct options are
A $16$
C $60$

We have 4 even positions - 2nd, 4th, 6th, 8th
4 odd digits - 3, 3, 5, 5
These 4 digits can be arranged in the 4 even positions in $\frac{4!}{2!\times 2!}$= 6 ways
Remaining 5 digits (2, 2, 8, 8, 8) can be arranged in 5 odd positions in $\frac{5!}{2!\times 3!}$ = 10 ways
Thus total ways $6\times 10=60$

Hence Option C is correct