Permutation With Repetition and Circular Permutations n n

Permutation With Repetition and Circular Permutations n n n Linear Permutations: arrangements in a line: n! Permutations involving Repetitions: n!/(p!q!) How many thirteen-letter patterns can be formed from the letters of the word differentiate? 13!/(2!2!3!2!) =129, 729, 600

Permutation With Repetition and Circular Permutations n n n Circular Permutations: No beginning or end. . . : (n-1)! Children on a Merry-Go-Round Fixed point of reference. . . considered Linear : n! Seating around a round table with one person next to a computer n If the circular permutation looks the same when it is turned over, such as a plain key ring, then the number of permutations must be divided by two.

Permutation With Repetition and Circular Permutations n During an activity at school, 10 children are asked to sit in a circle n Is the arrangement of children a linear or circular permutation? Explain. n arrangement is a circular permutation since the children sit in a circle and there is no reference point. n There are ten children so the number of arrangements can be described by (10 - 1)! or 9! 9! = 9 8 7 6 5 4 3 2 1 or 362, 880

Permutation With Repetition and Circular Permutations

Permutation With Repetition and Circular Permutations

Permutation With Repetition and Circular Permutations

Permutation With Repetition and Circular Permutations