Question 1019208: Use formula for Permutations to calculate in how many ways you can select 2 people out of 10, order of selection makes a difference.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! p(n,x) = n! / (n-x)!
n = 10
x = 2
p(n,x) becomes p(10,2) = 10! / (10-2)! = 10! / 8! = (10 * 9 * 8!) / 8!.
the 8! in the numerator and denominator cancel out and you are left with:
p(10,2) = 10 * 9 = 90
in the permutation formula, order makes a difference, so sets with the same elements but in different order are counted as separate sets.
in the combination formula, order does not make a difference, so sets with the same elements are only counted.
this can be seen easily when dealing with a smaller number of permutations and combinations.
assume n = 3 and x = 2.
permutation formula ia p(n,x) = n! / (n-x)!
combination formula is c(n,x) = n! / (x! * (n-x)!)
that extra division by x! in the combinattion formula takes away the multiple ordered versions of the same set.
p(3,2) = 3! / 1! = 3*2 = 6
c(3,2) = 3! / (2! * 1!) = (3*2)/2 = 3
assume the elements are a, b, and c.
the number of permutations of 2 out of the 3 elements are detailed below:
ab
ba
ab
ca
bc
cb
even though ab and ba have the same elements, they are in a different order and counted separately.
the number of combinations of 2 out of the 3 elements are detailed below:
ab
ac
bc
ba and ca and cb are not counted as separate sets because they are the same elements shown above but in a different order.
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