Chapter 12.6 Notes. O A positive integer n is the product of the positive integers less than or equal to n. 0! Is defined to be 1. n! = n ● (n -1) ● (n.

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Presentation transcript:

Chapter 12.6 Notes

O A positive integer n is the product of the positive integers less than or equal to n. 0! Is defined to be 1. n! = n ● (n -1) ● (n -2) ● … ● 1, where n > 1 O Example: 5! 5! = 5 ● 4 ● 3 ● 2 ● 1 = 120

O Each possible arrangement of a set of numbers or items, assuming that order is important.

O The number of permutations of n objects taken r at a time is the quotient of n! and (n- r)!. P(n, r) = n! (n-r)!

P(n, r) = n! (n-r)! O Example: P(10, 6) P(10, 6) = 10! (10-6)! = 10! 4! = 10 ●9 ●8 ●7 ●6 ●5 ●4 ●3 ●2 ●1 4 ●3 ●2 ●1 = 151,200

O A selection of objects in which order is not important.

O The number of combinations of n objects taken r at a time is the quotient of n! and (n- r)!r!. C(n, r) = n! (n-r)!r!

C(n, r) = n! (n-r)!r! O Example: C(8, 5) C(8, 5) = 8! (8-5)!5! = 8! 3!5! = 8 ● 7 ● 6 ● 5 ● 4 ● 3 ● 2 ● 1 3 ● 2 ● 1 ● 5 ● 4 ● 3 ● 2 ● 1 = = 56