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

The correct option is C

$60$

Find the total number of arrangements :

The given number is $223355888$. Since the condition is odd digits occupy even positions.

There are $9$places for $4$ digits.

$OEOEOEOEO$ where $O=$odd position and $E=$even position

There are $4$odd digits$:3,3,5,5,$that can be placed in $4!/(2!.2!)=6$ ways.

The five even digits, $2,2,8,8,8,$can be arranged in $5!/(2!.3!)=10$ways

Therefore, total number of arrangements $=6x10=60$ ways

Hence the correct option is C.