In how many ways 5 members forming a committee out of 10 be selected so that
2 particular members must not be included.

Answer

To solve the problem of selecting 5 members out of 10 such that 2 particular members are not included, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Members and Exclusions**:
We have a total of 10 members, but we need to exclude 2 particular members from our selection. This means we are left with \(10 - 2 = 8\) members.

2. **Determine the Number of Members to Select**:
We need to form a committee of 5 members from the remaining 8 members.

3. **Use the Combination Formula**:
The number of ways to choose \(r\) members from \(n\) members is given by the combination formula:
\[ nCr = \frac{n!}{r!(n-r)!} \]
In our case, we need to calculate \(8C5\).

4. **Calculate \(8C5\)**:
Using the combination formula:
\[ 8C5 = \frac{8!}{5!(8-5)!} = \frac{8!}{5! \cdot 3!} \]

5. **Simplify the Factorials**:
We can express \(8!\) as \(8 \times 7 \times 6 \times 5!\):
\[ 8C5 = \frac{8 \times 7 \times 6 \times 5!}{5! \cdot 3!} \]
The \(5!\) in the numerator and denominator cancels out:
\[ 8C5 = \frac{8 \times 7 \times 6}{3!} \]

6. **Calculate \(3!\)**:
\(3! = 3 \times 2 \times 1 = 6\).

7. **Final Calculation**:
Now we can substitute \(3!\) back into the equation:
\[ 8C5 = \frac{8 \times 7 \times 6}{6} \]
The \(6\) cancels out:
\[ 8C5 = 8 \times 7 = 56 \]

8. **Conclusion**:
Therefore, the number of ways to select 5 members from the remaining 8 members (excluding the 2 particular members) is \(56\).

### Final Answer:
The committee can be formed in **56 ways**.