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09-1 - Consider the following problem You are ordering a...

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Unformatted text preview: Consider the following problem: You are ordering a hamburger and can get up to 8 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 3 toppings? Here we are trying to figure out the probability that you will get 3 toppings on your hamburger. First, we need to realize that choosing 3 toppings out of 8 is a combination. Remember that a combination is used when order is not important. Written symbolically, n! C=—. " r r!(n—r)! Therefore, we will have 8C3 combinations of 3 toppings on the hamburger. Solving for the number of ways we can have 3 toppings on a hamburger, we get 8! 8! 40320 _(6)(120)_ C — 56. 8 3 3!(8—3)! _ 3!5! ...
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