Question

A veggie wrap at Dylan's Diner is composed of 3 different vegetables and 3 different condiments wrapped up in a tortilla. If there are 9 vegetables, 5 condiments, and 5 types of tortilla available, how many different veggie wraps can be made

Answer 1

`5C1 (9C3) (5C3)`

And replacing we got:

`(5!)/(1! 4!) ((9!)/(3! (9-3)!)) ((5!)/(3! (5-3)!)) = 5*84*10=4200`

So then we have a total of 4200 possibilities in order to have a veggle wrap

Explanation:

For this case we can use the combinatory formula given by:

`nCx= (n!)/(x! (n-x)!)`

And for this case we have a total of 9 vegatables and 5 condiments and 5 types of tortilla. Then the total number of possibilities are:

`5C1 (9C3) (5C3)`

And replacing we got:

`(5!)/(1! 4!) ((9!)/(3! (9-3)!)) ((5!)/(3! (5-3)!)) = 5*84*10=4200`

So then we have a total of 4200 possibilities in order to have a veggle wrap