Answer the questions below.(If necessary, consult a list of formulas.)(a) A pizza parlor has a choice of 12 toppings for its pizzas. From these 12 toppings, how many different 8-topping pizzas are possible?(b) From the 13 albums released by a musician, the recording company wishes to release 10 in a boxed set. How many different boxed sets are possible?
Question
Answer the questions below.(If necessary, consult a list of formulas.)(a) A pizza parlor has a choice of 12 toppings for its pizzas. From these 12 toppings, how many different 8-topping pizzas are possible?(b) From the 13 albums released by a musician, the recording company wishes to release 10 in a boxed set. How many different boxed sets are possible?
Solution
(a) The number of ways to choose 8 toppings from 12 is given by the combination formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of options, k is the number of options to choose, and "!" denotes factorial.
So, C(12, 8) = 12! / [8!(12-8)!] = 495 different 8-topping pizzas are possible.
(b) Similarly, the number of ways to choose 10 albums from 13 is given by the combination formula.
So, C(13, 10) = 13! / [10!(13-10)!] = 286 different boxed sets are possible.
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