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 a total of 15 players while excluding 2 specific players, we can follow these steps:

### Step 1: Determine the number of players available for selection
Since we need to exclude 2 particular players from the selection, we subtract these 2 players from the total of 15 players.

\[ \text{Available players} = 15 - 2 = 13 \]

### Step 2: Calculate the number of ways to select 11 players from the remaining 13 players
Now, we need to select 11 players from the 13 available players. This can be calculated using the combination formula \( nCr \), which is given by:

\[ nCr = \frac{n!}{r!(n-r)!} \]

In our case, \( n = 13 \) and \( r = 11 \). Therefore, we can write:

\[ 13C11 = \frac{13!}{11!(13-11)!} = \frac{13!}{11! \cdot 2!} \]

### Step 3: Simplify the combination
We can simplify \( 13C11 \) as follows:

\[ 13C11 = \frac{13 \times 12}{2 \times 1} \]

### Step 4: Calculate the value
Now we perform the calculations:

\[ 13C11 = \frac{13 \times 12}{2} = \frac{156}{2} = 78 \]

### Conclusion
Thus, the number of ways to select 11 players from the remaining 13 players, excluding the 2 particular players, is:

\[ \text{Total ways} = 78 \]

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