# Q. How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions?

(a) 12

(b) 18

(c) 36

(d) 72

Correct Answer: (c) 36

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## 8-Digit Number Arrangement – 11223344

The number 11223344 has 4 odd digits (1,1,3,3) and 4 even digits (2,2,4,4).

In an 8-digit number, there are 4 odd positions (1st, 3rd, 5th, 7th) and 4 even positions (2nd, 4th, 6th, 8th).

The 4 odd digits can be arranged in the 4 odd positions in 4!/2!2! = 6 ways (4 factorial divided by 2 factorial times 2 factorial, because there are 2 pairs of identical digits).

Similarly, the 4 even digits can be arranged in the 4 even positions in 4!/2!2! = 6 ways.

Therefore, the total number of distinct 8-digit numbers is 6 * 6 = 36.

So, the correct answer is (c) 36.