how to solve this problem : A veggie wrap at City Subs is composed of four different vegetables into 2 different condiments wrapped up in a tortilla. If there are 7 vegetables, 5 condiments, and six types of tortilla available, how many different veggie wraps can be made?

how to solve this problem A veggie wrap at City Subs is composed of four different vegetables into 2 different condiments wrapped up in a tortilla If there are class=

Respuesta :

Answer:

2100 different veggie wraps

Explanation:

We have 7 different vegetables, out of which we are choosing 4; therefore, the number of ways we can choose 4 out of 7 in unique ways is

[tex]C(7,4)=\frac{7!}{(7-4)!4!}=35[/tex]

Now for condiments, a veggie wrap uses two different condiments, therefore, the number of ways we can choose 2 out of 5 is

[tex]C(5,2)=\frac{5!}{(5-2)!2!}=10[/tex]

And we have 6 types of tortillas.

Therefore, the number of different veggie wraps that can be made is

[tex]35\times10\times6=2100[/tex]

In other words, 2100 different veggie wraps can be made.