The general formula for the number of combinations of r things chosen from n different things is C(n,r) = n!/ r!(n-r)! How many ways can 5 players be chosen from a team of 13?
(Where the order you choose the players does not matter).
So C(13,5) = 13!/5!(13-5)!
Or 1,287
There are 120 possible ways.
To calculate the number of permutations here, where order is important and repetition is not allowed, we use the following formula:
Number of permutations = n! / (n - r)! = 5!/0! = 1*2*3*4*5 / 1 (note: "!" means "factorial" and 0! equals 1) = 120/1 = 120.
For a complete list see below. Let a,b,c,d & e represent the 5 players and their order determine their position:
{a,b,c,d,e} {a,b,c,e,d} {a,b,d,c,e} {a,b,d,e,c} {a,b,e,c,d} {a,b,e,d,c} {a,c,b,d,e} {a,c,b,e,d} {a,c,d,b,e} {a,c,d,e,b} {a,c,e,b,d} {a,c,e,d,b} {a,d,b,c,e} {a,d,b,e,c} {a,d,c,b,e} {a,d,c,e,b} {a,d,e,b,c} {a,d,e,c,b} {a,e,b,c,d} {a,e,b,d,c} {a,e,c,b,d} {a,e,c,d,b} {a,e,d,b,c} {a,e,d,c,b} {b,a,c,d,e} {b,a,c,e,d} {b,a,d,c,e} {b,a,d,e,c} {b,a,e,c,d} {b,a,e,d,c} {b,c,a,d,e} {b,c,a,e,d} {b,c,d,a,e} {b,c,d,e,a} {b,c,e,a,d} {b,c,e,d,a} {b,d,a,c,e} {b,d,a,e,c} {b,d,c,a,e} {b,d,c,e,a} {b,d,e,a,c} {b,d,e,c,a} {b,e,a,c,d} {b,e,a,d,c} {b,e,c,a,d} {b,e,c,d,a} {b,e,d,a,c} {b,e,d,c,a} {c,a,b,d,e} {c,a,b,e,d} {c,a,d,b,e} {c,a,d,e,b} {c,a,e,b,d} {c,a,e,d,b} {c,b,a,d,e} {c,b,a,e,d} {c,b,d,a,e} {c,b,d,e,a} {c,b,e,a,d} {c,b,e,d,a} {c,d,a,b,e} {c,d,a,e,b} {c,d,b,a,e} {c,d,b,e,a} {c,d,e,a,b} {c,d,e,b,a} {c,e,a,b,d} {c,e,a,d,b} {c,e,b,a,d} {c,e,b,d,a} {c,e,d,a,b} {c,e,d,b,a} {d,a,b,c,e} {d,a,b,e,c} {d,a,c,b,e} {d,a,c,e,b} {d,a,e,b,c} {d,a,e,c,b} {d,b,a,c,e} {d,b,a,e,c} {d,b,c,a,e} {d,b,c,e,a} {d,b,e,a,c} {d,b,e,c,a} {d,c,a,b,e} {d,c,a,e,b} {d,c,b,a,e} {d,c,b,e,a} {d,c,e,a,b} {d,c,e,b,a} {d,e,a,b,c} {d,e,a,c,b} {d,e,b,a,c} {d,e,b,c,a} {d,e,c,a,b} {d,e,c,b,a} {e,a,b,c,d} {e,a,b,d,c} {e,a,c,b,d} {e,a,c,d,b} {e,a,d,b,c} {e,a,d,c,b} {e,b,a,c,d} {e,b,a,d,c} {e,b,c,a,d} {e,b,c,d,a} {e,b,d,a,c} {e,b,d,c,a} {e,c,a,b,d} {e,c,a,d,b} {e,c,b,a,d} {e,c,b,d,a} {e,c,d,a,b} {e,c,d,b,a} {e,d,a,b,c} {e,d,a,c,b} {e,d,b,a,c} {e,d,b,c,a} {e,d,c,a,b} {e,d,c,b,a}
Math I know; Basketball I'm a little weaker on.
Assuming that each of the five positions is distinct there are 8! / 3! or 6720 possible combinations.
Assuming that all of the five positions are the same (I know this isn't true; I'm just putting it up for comparison) there are 8 choose 5 ( 8!/(3!*5!)) or 56 possible combinations.
If some of the positions are the same but others aren't, then the answer is somewhere in between.
The first position can be filled by eight, the second by seven, and so on. So the number of possibilities are: 8!/3! = 8*7*6*5*4 = 6720
1
5
200
A typical basketball team has at least 5 members because 5 people are needed to be on the court to play the 5 positions.
There are 5 different positions on a basketball team. Point Guard, Shooting Guard, Small Forward, Power Forward, and Center
Their is five starting players.
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