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?

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.