CHAPTER XXXV.
Permutations and Combinations.
390. Each of the arrangements which can be made by taking some or all of a number of things is called a permutation.
Each of the groups or selections which can be made by taking some or all of a number of things is called a combination.
Thus the permutations which can be made by taking the letters a, b, c, d two at a time are twelve in number; namely,
ab, ac, ad, bc, bd, cd, ba, ca, da, cb, db, dc;
each of these presenting a different arrangement of two letters.
The combinations which can be made by taking the letters a, b, c, d two at a time are six in number; namely,
ab, ac, ad, be, bd, cd;
each of these presenting a different selection of two letters.
From this it appears that in forming combinations we are only concerned with the number of things each selection contains; whereas in forming permutations we have also to consider the order of the things which make up each arrangement; for instance, if from four letters a, b, c, d we make a selection of three, such as abc, this single combination admits of being arranged in the following ways:
abc, acb, bca, bac, cab, cba,
and so gives rise to six different permutations.
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