A committee of 5 is to be formed from a group of 10 people consisting 4 single men 4 single women and a married couple. The committee is to consist of a chairman , who must be a single man 2, other men and 2 women,
Find the total number of committes possible.

Answer

To solve the problem, we need to form a committee of 5 members consisting of a chairman (who must be a single man), 2 other men, and 2 women from a group of 10 people (4 single men, 4 single women, and 1 married couple).

Let's break down the solution step by step:

### Step 1: Choose the Chairman
The chairman must be a single man. Since there are 4 single men available, we can choose the chairman in:
\[ \text{Number of ways to choose the chairman} = \binom{4}{1} = 4 \]

### Step 2: Choose the Other Men
After selecting the chairman, we need to choose 2 other men. Since one single man has already been chosen as the chairman, we have 3 single men left to choose from. Thus, we can choose the other 2 men in:
\[ \text{Number of ways to choose 2 other men} = \binom{3}{2} = 3 \]

### Step 3: Choose the Women
Next, we need to choose 2 women from the 4 single women available. The number of ways to choose 2 women is given by:
\[ \text{Number of ways to choose 2 women} = \binom{4}{2} = 6 \]

### Step 4: Calculate the Total Number of Committees
Now, we multiply the number of ways to choose the chairman, the other men, and the women together to find the total number of committees possible:
\[ \text{Total number of committees} = \binom{4}{1} \times \binom{3}{2} \times \binom{4}{2} = 4 \times 3 \times 6 \]
Calculating this gives:
\[ 4 \times 3 = 12 \]
\[ 12 \times 6 = 72 \]

Thus, the total number of committees possible is:
\[ \boxed{72} \]