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