PINKLETES
PRODUCT PRINCIPLE
Also known as Counting by Stages, if X and Y are two independent things, (meaning one won't affect the other), and there are M number of options of X and N number of options for Y, then there are M x N number of ways for both thing to occur.
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Example: Suppose Suzy has to choose between 5 different flavors of ice-cream and 10 different toppings. How many combinations of ice-cream can suzy make?
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Answer: 5 x 10 = 50
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Explanation: Since ice-cream flavors and toppings are independent of each other, Suzy can chose from 5 ice-cream flavors and 10 different topping
What if X and Y are not independent of each other?
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Example: Suppose lucy can only choose 2 distinct flavors of ice-cream out of 5 different flavors. How many combinations of ice-cream can Suzy make?
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Answer: 5 x 4 = 20
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a b c d e
w x y z -----> (a,w) (a,x) (a,y) (a,z) (b,w) (b,x) (b,y) (b,z) (c,w) (c,x) (c,y) (c,z) (d,w) (d,x) (d,y) (d,z) (e,w) (e,x) (e,y) (e,z)
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Explanation: For her first flavor, Suzy has 5 different options to choose from. After choosing her first flavor Suzy now only has 4 different options remaining. Meaning there are 5 x 4 different combinations of ice-cream.
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