Lesson 4.4-4.5

# Lesson 4.4-4.5 - CountingRules HonorsStatistics...

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Counting Rules Honors Statistics Mr. Kenneth Horwitz Lessons 4.4 and 4.5

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n The  fundamental counting rule  is also called  the  multiplication of choices . n In a sequence of n events in which the first  one has  k 1 possibilities and the second event  has  k 2 and the third has  k 3, and so forth, the  total number of possibilities of the sequence  will be k 1 ∙  k 2 ∙  k 3 ∙ ∙ ∙  k n 4.4 Counting Rules
Example 4-39: Paint Colors A paint manufacturer wishes to manufacture several different  paints. The categories include Color:  red, blue, white, black, green, brown, yellow Type:  latex, oil Texture:  flat, semigloss, high gloss Use:  outdoor, indoor How many different kinds of paint can be made if you can  select one color, one type, one texture, and one use? ( 29 ( 29 ( 29 ( 29 # of # of # of # of colors types textures uses 7 2 3 2 × × × 84 different kinds of paint

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Counting Rules   n Factorial  is the product of all the positive  numbers from 1 to a number. n Permutation  is an arrangement of objects  in a specific order.  Order matters. ( 29 ( 29 ! 1 2 3 2 1 0! 1 n n n n = - - ××× × × = ( 29 ! ! n r n P n r = - ( 29 ( 29 ( 29 1 2 1 items n n n n r r = - - - + L 1 4 4 4 442 4 4 4 443
n Combination  is a grouping of objects.  Order  does not matter. ( 29

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