Question

out of 20 members in a family, 11 like to take tea and 14 like coffee. assume that each one likes atleast one of the two drinks. find how many like both coffee and tea:

Answer 1

Using the principle of inclusion-exclusion, we find that 5 family members like both coffee and tea.

Step-by-step explanation:

The question requires us to determine how many members of a family like both coffee and tea given that there are 20 family members, 11 like tea, and 14 like coffee, and each member likes at least one of the two drinks.

This is a classic problem that can be solved by using the principle of inclusion-exclusion.

According to the principle of inclusion-exclusion:

• Number who like tea or coffee = Number who like tea + Number who like coffee - Number who like both tea and coffee

Since each member likes at least one of the two, all 20 family members like tea or coffee.

Therefore: 20 = 11 + 14 - Number who like both tea and coffee

To find the number of family members who like both, we rearrange the equation:

Number who like both tea and coffee = 11 + 14 - 20 = 5

Hence, 5 members of the family like both coffee and tea.