Question

A barn has forty-eight sheep. Twenty-two sheep like to eat clover, twenty-two like to eat forbs, and seventeen like to eat grass. Eleven like to eat clover and grass, thirteen like to eat clover and forbs, and eleven like to eat forbs and grass. Nine like eating all three types of food. How many sheep do not eat any of the listed items?

Answer 1

Using the principle of inclusion and exclusion from set theory, we find that there are 13 sheep that do not eat any of the listed items from a total of 48 sheep.

Step-by-step explanation:

To find out how many sheep do not eat any of the listed items (clover, forbs, grass), we use the principle of inclusion and exclusion from set theory in mathematics. We start with the total number of sheep, and subtract the numbers of sheep that have specific eating preferences, adjusting for those sheep that eat multiple foods.

1. First, we add up the number of sheep that eat each type of food: 22 (clover) + 22 (forbs) + 17 (grass) = 61. However, some sheep are counted multiple times because they like more than one type of food.
2. We then subtract the sheep that are double-counted for eating two types of food: 61 - 11 (clover and grass) - 13 (clover and forbs) - 11 (forbs and grass) = 26.
3. Next, we add back the sheep that were triple-counted for eating all three types of food: 26 + 9 = 35.
4. Finally, we subtract this number from the total number of sheep to find out how many do not eat any of the listed foods: 48 (total sheep) - 35 = 13 sheep.

Therefore, there are 13 sheep that do not eat clover, forbs, or grass.