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43 votes
43 votes
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-example-1
User Andreyco
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2.9k points

1 Answer

29 votes
29 votes

Answer

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

User Suemayah Eldursi
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3.0k points