Explanation
1. Step 1: Seating the Women
There are 2 women who need to sit.
They must choose from the chairs numbered 1 to 4 (a total of 4 available chairs).
Since the chairs are numbered uniquely, the order in which they sit matters (this is an arrangement problem, not just selection).
The number of ways to arrange 2 women on 4 distinct chairs is given by the permutation formula:
Ways for women=4P2
2. Step 2: Determining Remaining Chairs
Total chairs available initially = 8
Number of chairs occupied by the 2 women = 2
Therefore, the remaining number of empty chairs left in the room is:
8−2=6 chairs
3. Step 3: Seating the Men
There are 3 men who need to sit.
They must select their seats from amongst any of the 6 remaining chairs.
The number of ways to arrange 3 men on 6 distinct remaining chairs is:
Ways for men=6P3
4. Step 4: Total Number of Possible Arrangements
By the Fundamental Principle of Counting, the total number of independent ways to complete both events together is the product of the possibilities of each individual step:
Total Arrangements=Ways for women×Ways for men
Total Arrangements=4P2×6P3
Thus, option (d) is the correct answer.
