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

24024 ways

Step-by-step 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:

`(14!)/(1!*6!*7!)=(14*13*12*11*10*9*8*7!)/(1*6*5*4*3*2*1*7!)=(17297280)/(720)=24024\text{ }ways`