How many different teams of 11 players can be chosen from a soccer squad of 16?

Answer 1

The number of different teams of 11 players that can be chosen from a soccer squad of 16 can be calculated using the combination formula, which is expressed as:

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

In this case, n = 16 (number of players in the squad) and r = 11 (number of players needed for a team).

Plugging the values into the formula:

C(16, 11) = 16! / (11! * (16-11)!)
= 16! / (11! * 5!)

Now, let's calculate the factorial of each number:

16! = 16 * 15 * 14 * 13 * 12 * 11!
5! = 5 * 4 * 3 * 2 * 1

Simplifying the expression:

C(16, 11) = (16 * 15 * 14 * 13 * 12 * 11!) / (11! * (5 * 4 * 3 * 2 * 1))
= (16 * 15 * 14 * 13 * 12) / (5 * 4 * 3 * 2 * 1)
= 43680 / 120
= 364

Therefore, there are 364 different teams of 11 players that can be chosen from a soccer squad of 16.

Answer 2

are you sure

Answer 3

Apologies for the incorrect answer. Let's recalculate it correctly:

The number of different teams of 11 players that can be chosen from a soccer squad of 16 can be calculated using the combination formula:

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

Plugging in the values:

C(16, 11) = 16! / (11! * (16-11)!)
= 16! / (11! * 5!)

Calculating the factorials:

16! = 16 * 15 * 14 * 13 * 12 * 11!
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
5! = 5 * 4 * 3 * 2 * 1

Simplifying the expression:

C(16, 11) = (16 * 15 * 14 * 13 * 12 * 11!) / (11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= (16 * 15 * 14 * 13 * 12) / (5 * 4 * 3 * 2 * 1)
= 43680 / 120
= 364

Therefore, there are indeed 364 different teams of 11 players that can be chosen from a soccer squad of 16.