Mathematics Dictionary Dr. K. G. Shih

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Permutation

Symbol Defintion Example : Sqr(x) = square root of x

Q01 | - Permutation Q02 | - Permutation of 3 digits Q03 | - Ten people in a line Q04 | - Ten people in a circle Q05 | - References

Q01. Permutation Definition There are n different symboals Each time take r What is the permuatation ? 1. No repeating : P(n,r) = n*(n-1)*(n-2)*....*(n-r+1) 2. With repeating : Permuation = n^r Go to Begin Q02. Permutation of 3 digits How many 3 digit number can be made ? No zero in 3 digits 1. No repeating : 3! = 6 2. With repeating : 3^3 = 27 Zero is included in the 3 digits 1. No repeating : 3! - 2! = 4 (2! is zero at left side) 2. With repeating : 3^3 - 2^2 = 27 - 4 = 23 (2^2 is zero at left side) Illustration : 3 digits are 1, 2, 3 No repeating Permuatation is 6 123, 132, 231, 213, 312, 321 With repeating Arrangement is 27 123, 132, 231, 213, 312, 321 112, 121, 211, 113, 131, 311 223, 232, 322, 221, 212, 122 331, 313, 133, 332, 323, 233 111, 222, 333 Go to Begin Q03. Ten people in a line One person fixed at 1st position and 2nd person fixed at end The arrangemet is (10 - 2)! = 8! = 40320 Go to Begin Q04. Ten people in a circle Find arrangement (10 - 1)! = 9! = 362880 Go to Begin Q4. References Reference : Numbers Program 16 : Find P(n,r) Go to Begin

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