Respuesta :
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
