Question

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 county fair arrange the pens for the horses and cows in the same barn? How the quantities given in the problem relate to each other?

Answer 1

1 . 60!=8.31*
`10^(81)` ways

The rows and number of barns are related in that if we want to get the number of ways the cows and horse can be arranged

Explanation:

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 county fair arrange the pens for the horses and cows in the same barn? How the quantities given in the problem relate to each other?

if there are 10 ros and 6 barns. the number of ways animsls can be arrganged becomes

10 *6=60

60

look for 60 factorials, the number of ways

60!=8.31*
`10^(81)` ways

2.Permutation means arrangement . The rows and number of barns are related in that if we want to get the number of ways the cows and horse can be arranged , it makes it possible

For example find the number of ways 12 cows and 18 horses can be arranged in the barns.

we have the number of animals to be=12+18=30

60P30=60
`(60!)/(960-30)!) =(60!)/(30!)`

31.37*10^48 ways