Question

A veggie wrap at City Subs is composed of 3 different vegetables and 3 different condiments wrapped up in a tortilla. If there are 8 vegetables, 8 condiments, and 5 types of tortilla available, how many different veggie wraps can be made?

Answer 1

Answer:

560 veggie wraps can be made.

Step-by-step explanation:

Given:

Number of vegetables available = 8

Number of vegetables needed to make a veggie wrap = 3

Number of condiments available = 5

Number of condiments required to make a veggie wrap = 3

Now, selecting 3 vegetables from a total of 8 vegetables is given as the combination of 3 out of 8 which is equal to $_{3}^{8}\textrm{C}$

Now, selecting 3 condiments from a total of 5 condiments is given as the combination of 3 out of 5 which is equal to $_{3}^{5}\textrm{C}$

Now, the veggie wrap must have both vegetables and condiments. Therefore, the total number of different combinations of veggie wraps is equal to the product of their individual combinations.

Number of different veggie wraps possible is given as:

$N=_{3}^{8}\textrm{C}\times _{3}^{5}\textrm{C}$

We know that, $_{r}^{n}\textrm{C}=\frac{n!}{r!(n-r)!}$

Expanding using the combination formula, we get:

$N=\frac{8!}{3!\times 5!}\times \frac{5!}{3!\times 2!}\\\\N=\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1\times3\times 2\times 1\times 2\times 1}\\\\N=\frac{6720}{12}=560$

Therefore, 560 veggie wraps can be made.