Question

a veggie wrap at City Subs is composed of four different vegetables into different condiments wrapped up in a tortilla. If there are 7 vegetables, five condiments, and six types of tortilla available, how many different veggie wraps can be made?

Answer 1

The veggie wraps can be made in 1050 ways

Explanation:

Total number of vegetables = 7

Number of Tortilla available = 6

Number of condiments = 5

7C4 x 5C4 x 6

The number of ways it could be arranged is

`\begin{gathered} 7C4\cdot\text{ 5C4 }\cdot6 \\ 7C4\text{ = }\frac{7!}{(7\text{ - 4)!4!}} \\ 7C4\text{ = }\frac{7\text{ x 6 x 5 x 4 x 3 x 2 x 1}}{3\text{ x 2 x 1! 4 x 3 x 2 x 1}} \\ 7C4\text{ = }\frac{7\text{ x 6 x 5}}{6} \\ 7C4\text{ = 35} \\ \\ 5C4\text{ =}\frac{\text{ 5 x 4 x 3 x 2 x 1}}{\text{ 1! 4 x 3 x 2 x 1}} \\ 5C4\text{ = }\frac{\text{ 5}}{1} \\ 5C4\text{ = 5} \\ \\ 35\text{ x 5 x 6} \\ =1050\text{ ways} \end{gathered}`

Hence, the veggie wraps can be made in 1050 ways