exclusion inclusion problem

q)**There are 323 farms in a country that have atleast one of horses cows and sheep.if 224 have horses 85 have cows 57 have sheep and 18 farms have all three types of animals.how many farms have exactly 2 of these 3 typrs of animals?**

solution:

A farm hve horses=224

B farm have horses=57

C farm have horses=18

|AUBUC|=323

By using inclusion exclusion principle ,we have

|AUBUC|=|A| + |B| +|C| -|A intersection B| -|A INTERSECTION C| - |B intersection C|+|A INTERSECTION B INTERSECTION C|

324=224 + 85 +57 +18 -|A intersection B| -|A INTERSECTION C| - |B intersection C|

|A intersection B| +|A INTERSECTION C| + |B intersection C| =60

which our required solution

please tell me if i am right or wrong

Re: exclusion inclusion problem

Hi,

Your solution looks fine to me.