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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

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 arran class=

Respuesta :

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:

[tex]\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[/tex]