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Jenny is arranging 12 cans of food in a row on a shelf. She has 5 cans of beans, 1 can of carrots, and 6 cans of corn. In how many distinct orders can the cans
be arranged if two cans of the same food are considered identical (not distinct)?​

Respuesta :

thaovtp1407

Answer:

5544 ways

Step-by-step explanation:

Given that:

Number of cans = 12 (n)

Number of cans of corns = 6  ([tex]r_{1}[/tex])

Number of cans of carrot = 1  [tex]r_{2}[/tex]

Number of cans of beans = 5 [tex]r_{3}[/tex]

The number of different arrangements is given as:

[tex]\frac{n!}{r_{1}!\times r_{2}!\times ...r_{k}!}[/tex] where [tex]r_{1}[/tex] objects are of one kind, [tex]r_{2}[/tex] objects are of another and so on

We have: [tex]\frac{12!}{6!1!5!}[/tex] = 5544 ways  

Hope it will find you well.

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