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How many ways can 5 basketball players be placed in 5 positions?

source : answers.com

How many ways can 5 basketball players be placed in 5 positions?

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}

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