VJesus12 wrote: ↑

Fri Dec 17, 2021 10:26 am

Five friends - Ross, Phoebe, Chandler, Joey, and Monica - decide to have lunch at a pizzeria. Five types of individual pizza are available: Hawaiian, Supreme, Veggie, Pepperoni, and Margherita. If Ross refuses to eat Hawaiian, Phoebe will only eat Margherita, and no two friends will eat the same type of pizza, in how many ways can they order lunch?

A. 18
B. 24
C. 48
D. 96
E. 120

Answer: A

Source: Veritas Prep

Take the task of feeding the 5 friends and break it into stages.

We’ll begin with the most restrictive stage(s).

Stage 1: Select a pizza for Phoebe
Since Phoebe will only eat Margherita pizza, there's only 1 pizza we can serve her.
So, we can complete stage 1 in 1 way

Stage 2: Select a pizza for Ross
There are 4 pizzas remaining, but 1 of them is Hawaiian (which Ross refuses to eat).
So, there are only 3 pizzas we can serve Ross
We can complete stage 2 in 3 ways

Stage 3: Select a pizza for Chandler
There are 3 pizzas remaining, so we can complete stage 3 in 3 ways

Stage 4: Select a pizza for Joey
There are 2 pizzas remaining, so we can complete stage 4 in 2 ways

Stage 5: Select a pizza for Monica
There's only 1 pizza remaining, so we can complete stage 5 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus feed these "friends") in (1)(3)(3)(2)(1) ways (= 18 ways)

Answer: A