permutation and combination
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A permutation is the choice of r things from a set of n things without replacement and where the order matters. A combination is the choice of r things from a set of n things without replacement and where order does not matter.
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The different arrangements of a given number of things by taking some or all at a time, are called permutations.
Examples:
All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac,ca, bc, cb).
All permutations made with the letters a, b, c taking all at a time are:
( abc, acb, bac, bca, cab, cba)
Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination. Examples: Suppose we want to select two out of three boys A, B, C. Then, possible selections are AB, BC and CA. Note: AB and BA represent the same selection. All the combinations formed by a, b, c taking ab, bc,ca. The only combination that can be formed of three letters a, b, c taken all at a time is abc. Various groups of 2 out of four persons A, B, C, D are: AB, AC, AD, BC, BD, CD. Note that ab ba are two different permutations but they represent the same combination.
Examples:
All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac,ca, bc, cb).
All permutations made with the letters a, b, c taking all at a time are:
( abc, acb, bac, bca, cab, cba)
Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination. Examples: Suppose we want to select two out of three boys A, B, C. Then, possible selections are AB, BC and CA. Note: AB and BA represent the same selection. All the combinations formed by a, b, c taking ab, bc,ca. The only combination that can be formed of three letters a, b, c taken all at a time is abc. Various groups of 2 out of four persons A, B, C, D are: AB, AC, AD, BC, BD, CD. Note that ab ba are two different permutations but they represent the same combination.
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