Question

Permutation and combination formula list

Answer 1

One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: P(n,r)=n!(n−r)! A code have 4 digits in a specific order, the digits are between 0-9.
Factorial Notation:Let n be a positive integer. Then, factorial n, denoted n! is defined as:n! = n(n - 1)(n - 2) ... 3.2.1.Examples:We define 0! = 1.4! = (4 x 3 x 2 x 1) = 24.5! = (5 x 4 x 3 x 2 x 1) = 120.Permutations: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)Number of Permutations:Number of all permutations of n things, taken r at a time, is given by:nPr = n(n - 1)(n - 2) ... (n - r + 1) =n!(n - r)!Examples:6P2 = (6 x 5) = 30.7P3 = (7 x 6 x 5) = 210.Cor. number of all permutations of n things, taken all at a time = n!.An Important Result:If there are n subjects of which p1 are alike of one kind; p2 are alike of another kind; p3 are alike of third kind and so on and pr are alike of rth kind, 
such that (p1 + p2 + ... pr) = n.Then, number of permutations of these n objects is =n!(p1!).(p2)!.....(pr!)Combinations: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.Number of Combinations:The number of all combinations of n things, taken r at a time is:nCr =n!=n(n - 1)(n - 2) ... to r factors.(r!)(n - r)!r!Note:nCn = 1 and nC0 = 1.nCr = nC(n - r)Examples:i.   11C4 =(11 x 10 x 9 x 8)= 330.(4 x 3 x 2 x 1)ii.   16C13 = 16C(16 - 13) = 16C3 =16 x 15 x 14=16 x 15 x 14= 560.3!3 x 2 x 1

Answer 2

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