Probability and Permutations
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Key Questions

Permutations of items are arrangements of items.
Examples
All six permutations of
#{a,b,c}# are:#{abc, acb, bac, bca, cab, cba}# Also, all 6 permutations of
#{a,b,c}# chosen at 2 items at a time are#{ab, ba, ac, ca, bc, cb}#
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Permutations are arrangements of items, so the number of permutations is the number of arrangements of items.
Let
#P(n,r)# denote the number of permutations of#n# items chosen#r# items at a time.#P(n,r)# can be found by#P(n,r)=n cdot (n1) cdot (n2)cdot cdots cdot(nr+1)={n!}/{(nr)!}# .
Example
How many 3digit codes are possible if each digit is chosen from 0 through 9, and no digits are repeated.
We can think of 3digits codes as permutations of
#10# digits chosen#3# digits at a time since no digits are repeated. So, we have#P(10,3)=10 cdot 9 cdot 8=720# .Hence, there are 720 possible 3digit codes.
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It is important in permutations by the definition of the word "permutation". If we ignore order, then we are discussing / choosing "combinations".
Given set
#{a, b, c, d}# , if we count#ab# and#ba# as the same, then we are counting combinations.
If they are counted as different, then we are counting permutation. 
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