Question

medal if you check

A pizza place offers 5 different cheeses and 10 different toppings. In how many ways can a pizza be made with 2 cheese and 3 toppings?



1200


1000


800


600

so I know you go

5!/2!*3! = 10
10!/3!*7! =120

would the answer be 1200 right? I have never done this before we two things before. just want to make sure!

Answer 1

Since order does not matter, this is a combination problem.
To pick 2 cheeses out of 5, you have \(_5C_2\)
To pick 3 toppings out of 10, you need \(_{10}C_3\)
To find the total number, multiply those results.
\(_5C_2 \times _{10}C_3 = \dfrac{5!}{(5 - 2)!2!} \times \dfrac{10!}{(10 - 3)!3!} \)

\(= \dfrac{5!}{3!2!} \times \dfrac{10!}{7!3!} = \dfrac{5 \times 4}{2} \times \dfrac{10 \times 9 \times 8}{3 \times 2}\)

\(= 10 \times 120 = 1200\)

Answer 2

You are correct.

Answer 3

@mathstudent55 thanks so much!

Answer 4

You're welcome.