Six friends go to a pizza corner where there are 2 types of pizza, each…
Six friends go to a pizza corner where there are 2 types of pizza, each available in 6 different flavors. They must select 2 flavors of the same type of pizza from its 6 flavors. In how many ways can they select the pizza?
Answer: D. 30 ways — When items are selected from a set without regard to the order in which they are picked, the number of ways to choose r items from n distinct items is the…
- A.
60 ways
- B.
12 ways
- C.
15 ways
- D.
30 ways
Attempted by 5 students.
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Correct answer: D
When items are selected from a set without regard to the order in which they are picked, the number of ways to choose r items from n distinct items is the combination 6C2 = 6!/(2!·4!). When a choice is made from among several independent, mutually exclusive categories, the total number of ways is the sum of the ways available within each category.
Each pizza type offers 6 distinct flavors, and 2 flavors are chosen from a single type without regard to their order — this is a combination, not a permutation.
For one pizza type, the number of ways to choose 2 flavors out of 6 is 6C2 = 6!/(2!·4!) = 15.
Since there are 2 pizza types, and either one can be the type the flavors are drawn from, this count of 15 applies independently to each of the 2 types.
Adding the ways across both types: 15 + 15 = 30 ways in total.
Equivalently, the 2 independent decisions — which of the 2 pizza types to draw from, and which 2 flavors to pick from that type's 6 — combine by the counting principle: 2 × 15 = 30, the same total.