Question

How many different nine-digit numbers can be formed from the number $22,33,55,888$by rearranging its digits so that the odd digits occupy even positions?

• A. $16$
• B. $4$
• C. $60$
• D. $5$

Answer 1

The correct option is C

$60$

Explanation for the correct option:

Find the number of digits that can be formed :

In a nine-digit number, we have four even positions and five odd positions alternatively.

Therefore, we can mention $33,55$in even $4$ even positions in $4!/2!.2!$ ways $=6$ ways

Now, $22,888$ can be arranged in $5$ odd positions in $5!/2!.3!$ways $=10$ways

Thus,total number of ways $=6x10=60$ways.

Hence the correct option is C.