How many committees of 5 members each can be formed with 8 officials and 4 non - official members in the following cases:
each consits of 3 officials and 2 non - official members.

Answer

To solve the problem of how many committees of 5 members each can be formed with 8 officials and 4 non-official members, where each committee consists of 3 officials and 2 non-official members, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Members**:
We have 8 official members and 4 non-official members, making a total of 12 members (8 + 4 = 12).

2. **Determine the Composition of the Committee**:
Each committee must consist of 5 members, specifically 3 officials and 2 non-official members.

3. **Calculate the Number of Ways to Choose Officials**:
We need to select 3 officials from the 8 available officials. This can be calculated using the combination formula \( \binom{n}{r} \), which is given by:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
Thus, the number of ways to choose 3 officials from 8 is:
\[ \binom{8}{3} = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56 \]

4. **Calculate the Number of Ways to Choose Non-Officials**:
Next, we need to select 2 non-official members from the 4 available non-official members. Using the combination formula again, we have:
\[ \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 \]

5. **Combine the Results**:
To find the total number of committees, we multiply the number of ways to choose the officials by the number of ways to choose the non-officials:
\[ \text{Total Committees} = \binom{8}{3} \times \binom{4}{2} = 56 \times 6 = 336 \]

### Final Answer:
The total number of committees of 5 members each that can be formed with 3 officials and 2 non-official members is **336**.