Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4, and then the men select th chairs from amongst the remaining. The number of possible arrangements is a.`^6C_3xx^4C_2` b. `^4P_2xx^4P_3` c. `^4C_2xx^4P_3` d. none of these

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Selecting Chairs for Women
The first step is to select chairs for the two women from the four available chairs (numbered 1 to 4). The number of ways to choose 2 chairs from 4 is given by the combination formula \( C(n, r) \), which is \( C(4, 2) \).

\[ C(4, 2) = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 \]
...