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At the county fair animals are judged for the quality of their breeding and health.The animal pens are arranged in an array with one animal in each pen.A barn can hold at most 10 rows of pens and at most 6 pens in each row with room for people to walk around them.What different ways can the planners of the county fair arrange the pens for the horses and cows in the same barn? If 18 horses and 22cows are there

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JannetPalos

Answer:

[tex]\frac{60!}{20!}[/tex] ways

Step-by-step explanation:

Each row of the barn can hold at most 10 rows of pens and each row can contain at most 6 pens.

A pen can contain exactly one animal.

So, each barn can hold at most 1 × 6 × 10 = 60 animals.

Available animals in the county fair = 22 cows + 18 horses = 40

40 animals can be arranged in 60 places in [tex]60P_{40}[/tex]

= [tex]\frac{60!}{(60-40)!}[/tex]

= [tex]\frac{60!}{20!}[/tex] ways

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