How many different teams of 7 players can be chosen from 10 players?

To determine how many different teams of 7 players can be chosen from a group of 10 players, we can use the concept of combinations. Combinations are used when the order of selection does not matter.

Combination Formula

The formula for combinations is:

C(n, r) = n! / (r! * (n - r)!)

Where:

• n = total number of items (players)
• r = number of items to choose (team size)
• ! = factorial, which is the product of all positive integers up to that number

Applying the Formula

In this case:

• n = 10 (total players)
• r = 7 (players to choose)

Now, plug these values into the formula:

C(10, 7) = 10! / (7! * (10 - 7)!)

This simplifies to:

C(10, 7) = 10! / (7! * 3!)

Calculating Factorials

Now, calculate the factorials:

• 10! = 10 × 9 × 8 × 7!
• 3! = 3 × 2 × 1 = 6

Substituting back, we get:

C(10, 7) = (10 × 9 × 8) / 6

Final Calculation

Now, calculate:

10 × 9 × 8 = 720

Then divide by 6:

720 / 6 = 120

Result

Therefore, the number of different teams of 7 players that can be chosen from 10 players is 120.