In a group of 40 persons, 10 drink tea but not coffee and 26 drink tea. How many drink coffee but not tea?

Given:

Total number of persons: n(T ∪ C) = 40

Persons who drink tea: n(T) = 26

Persons who drink tea but not coffee: n(T - C) = 10

Persons who drink coffee only = n(C - T) = ?

First find number of persons who drink both tea and coffee by using the formula:

n(T ∩ C) = n(T) - n(T - C)

Substituting the values in above, we get:

n(T ∩ C) = 26 - 10

n(T ∩ C) = 16

So, 16 persons drink both tea and coffee.

Since every person in the group of 40 drinks at least one of the two beverages, the total is the sum of “tea only,” “coffee only,” and “both.”

n(T ∪ C) = n(T - C) + n(C - T) + n(T ∩ C)

n(C - T) = n(T ∪ C) - n(T - C) - n(T ∩ C) $\quad$[Solving for n(C - T)]

Substituting the values in above, we get:

n(C - T) = 40 - 10 - 16

n(C - T) = 40 - 26

n(C - T) = 14

∴ Number of persons who drink coffee but not tea = 14.

The Venn diagram is shown below: