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Introduction..... Symbols..... Permutations..... Permutations with repetition..... Combinations..... Combinations with repetition.....
A permutation is an arrangement of things with the order being important. abcd is different to bcda. A combination is a selection of things e.g. abcd is the collection of the four letters with no relevance given to the order.   If a team of eleven players are selected for a football team out of a selection of 20 persons with no importance given to the positions then the selection is combination. However if each position (goalkeeper, left fullback etc. ) is chosen seperately then the selection is a permutation.
Permutations and combinations
Permutations: (Without Repitition)
Permutation illustrates the number of ways to arrange elements in a definite order.
n! = 1.2.3 .....n (N Factorial)
The number of permutations of n elements of same kind taken r at a time.
nP(r) = n ! /(n-r)!
a,b,c / a,b,d /a,c,b /a,c,d / a,d,b/ a,d,c
Permutations: (With Repetition)
A Permutation with repetition is the number of ways to arrange
elements in a definite order allowing elements to be repeated.
nP(r) (with repetition) = n r
a,a / a,b / a,c / b,b /b,a / b,c/ c,c /c,a / c,b
A combination is the number of ways to arrange elements with no definite order. The number of combinations of n elements of same kind taken r at a time.
a,b,c / a,b,d /a,c,d /b,c,d
Combinations: with repetition
Combinations with repetition are the number of ways to arrange elements with no definite order but the elements can be repeated. The number of combinations of n elements of same kind taken r at a time.
a,a /a,b / a,c / b,b / b,c/ c,c /
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Last Updated 21/09/2007