There are fifteen players for a cricket match
In how many ways the 11 players can be selected excluding two particular players?

Answer

To solve the problem of selecting 11 players from 15 while excluding 2 particular players, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Total Players and Excluded Players**:
- We have a total of 15 players.
- We need to exclude 2 particular players from selection.

2. **Calculate the Remaining Players**:
- After excluding the 2 players, we have:
\[ 15 - 2 = 13 \text{ players remaining} \]

3. **Determine the Number of Players to Select**:
- We need to select 11 players from these remaining 13 players.

4. **Use the Combination Formula**:
- The number of ways to choose \( r \) players from \( n \) players is given by the combination formula:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
- In our case, \( n = 13 \) and \( r = 11 \). Thus, we need to calculate:
\[ \binom{13}{11} \]

5. **Simplify the Combination**:
- We can also use the property of combinations:
\[ \binom{n}{r} = \binom{n}{n-r} \]
- Therefore:
\[ \binom{13}{11} = \binom{13}{2} \]

6. **Calculate \( \binom{13}{2} \)**:
- Using the combination formula:
\[ \binom{13}{2} = \frac{13!}{2!(13-2)!} = \frac{13!}{2! \cdot 11!} \]
- This simplifies to:
\[ \frac{13 \times 12 \times 11!}{2! \times 11!} \]
- The \( 11! \) cancels out:
\[ = \frac{13 \times 12}{2!} \]

7. **Calculate \( 2! \)**:
- \( 2! = 2 \times 1 = 2 \)

8. **Final Calculation**:
- Now substituting back:
\[ = \frac{13 \times 12}{2} = \frac{156}{2} = 78 \]

9. **Conclusion**:
- Therefore, the number of ways to select 11 players from the remaining 13 players, excluding the 2 particular players, is:
\[ \boxed{78} \]