Question

In how many ways can a cricket eleven be chosen out of a batch of 15 players?

• A. 1000
• B. 1665
• C. 225
• D. 1365

Answer 1

The Correct Option is D

Step 1: The number of ways to choose 11 players from 15 is given by the combination formula: 

\[ {}^{15}C_{11} = {}^{15}C_{4} \]

Step 2: Calculate \( {}^{15}C_{4} \):

\[ {}^{15}C_{4} = \frac{15 \times 14 \times 13 \times 12}{4 \times 3 \times 2 \times 1} \]

\[ = 1365 \]