Question

A restaurant lunch special allows the customer to choose four vegetables from the following group. Peppers, spinach, corn, cauliflower, peas. How many outcomes are possible if the customer chooses four different vegetables?

Answer 1

There are 5 types of vegetables to choose from (peppers, spinach, corn, cauliflower, and peas), and the customer has to pick 4 different vegetables (no repetition). Therefore, the number of possible combinations when choosing 4 options out of 5 possibilities without repetition is

`5*(5-1)*(5-2)*(5-3)=5*4*3*2=5!=120`

However, notice that the order actually does not matter. Choosing peas and then corn must be equivalent to choosing corn and then peas.

Thus, the possible number of outcomes is

`(5!)/(4!(5-4)!)=(5)/(1!)=5`

The answer is 5 possible outcomes provided tha