In how many ways can a team of 10 basketball players be chosen from 12 players

To determine how many ways a team of 10 basketball players can be chosen from a group of 12, we need to calculate a **combination** because the order in which the players are chosen does not matter. The formula for combinations is given by:

\[
\text{Combination} = \binom{n}{r} = \frac{n!}{r!(n-r)!}
\]

Where:
- \( n \) is the total number of players (12 in this case).
- \( r \) is the number of players to choose (10 in this case).

Thus, the combination is:

\[
\binom{12}{10} = \frac{12!}{10!(12-10)!} = \frac{12!}{10!2!}
\]

Now, we can simplify this:

\[
\binom{12}{10} = \frac{12 \times 11}{2 \times 1} = \frac{132}{2} = 66
\]

So, there are **66 ways** to choose a team of 10 basketball players from 12 players.

Would you like further details or have any questions?

Here are 5 related questions for you:
1. How would the solution change if we needed to choose 8 players instead of 10?
2. What if we are choosing a team of 5 players from 12?
3. How would the answer differ if the order of selection mattered (i.e., permutations)?
4. Can you explain the difference between combinations and permutations?
5. How many ways can you choose 11 players from the same group of 12?

**Tip**: When choosing "n - r" items from "n", it's often easier to calculate \(\binom{n}{r} = \binom{n}{n-r}\) to reduce complexity.

In how many ways can a team of 10 basketball players be chosen from 12 players?

Discover how to calculate the number of ways to choose 10 basketball players from a group of 12 using the combination formula. This step-by-step guide explains the key concept of combinations and applies the formula to solve the problem, resulting in 66 possible teams. Ideal for students in Grades 9-12.

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