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A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible two-topping pizzas (2 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with banana peppers and Kalamata olives. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Sagot :

Using the combination formula, it is found that there is a [tex]\frac{1}{78}[/tex] probability that the first winner randomly selects the card for the pizza topped with banana peppers and Kalamata olives.

The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Researching the problem on the internet, it is found that 2 toppings will be chosen from a set of 13, hence:

[tex]C_{13,2} = \frac{13!}{2!11!} = 78[/tex]

The pizza topped with banana peppers and Kalamata olives is one outcome, hence:

p = 1/78.

There is a [tex]\frac{1}{78}[/tex] probability that the first winner randomly selects the card for the pizza topped with banana peppers and Kalamata olives.

More can be learned about the combination formula at https://brainly.com/question/25821700

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