Combinations And PermutationsWith combinations and permutations we are trying to determine the number of arrangements that can be made from a set of items dividing them into specific numbers or groups.In permutations, the order of items is all that is important ; we count x, y, z as different from y, z, x. But in combinations we are concerned only that x, y and z have been selected, regardless of order; x, y, z and y, z, x are the same combination. There are thus more permutations than combinations. n_C_x represents the number of combinations of n items taken x at a time. n_P_x represents the number of permutations of n items taken x at a time. How are combinations and permutations related? In general, n_C_x = n_P_x / x! (x factorial). For example:
5_P_3= 5! / (53)! = 5!/2! = 5*4*3*2*1/(2*1)=60 The number of Combinations of 5 items taken 3 at a time can be written as :
= 5! / (53)! / 3!
= 5! / (2! * 3!)
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