Question

Josh is arranging 14 cans of food in a row on a shelf. He has 1 can of olives, 6 cans of peas, and 7 cans of corn. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical

Answer 1

Answer

24024 ways

Explanation

Given:

1 olive can

6 pea cans

7 corn cans

What to find:

The number of distinct orders the cans can be arranged if two cans of the same food are considered identical.

Step-by-step solution:

They can be arranged using the formula below:

$\frac{14!}{1!\times6!\times7!}=\frac{14\times13\times12\times11\times10\times9\times8\times7!}{1\times6\times5\times4\times3\times2\times1\times7!}=\frac{17297280}{720}=24024\text{ }ways$