Question

In a class of 25 members, 15 take history, 17 take geography and 3 take neither subject. How many class members take both subjects?

Answer 1

In the class of 25 members, with 15 taking history, 17 taking geography, and 3 taking neither, 13 class members take both subjects according to the principle of inclusion-exclusion.

Step-by-step explanation:

To determine the number of class members that take both history and geography, we can use the principle of inclusion-exclusion. The formula is:

Total = (Number taking History) + (Number taking Geography) - (Number taking Both) + (Number taking Neither)

Since we are given that the class has 25 members, 15 take history, 17 take geography, and 3 take neither, we plug these values into the formula:

25 = 15 + 17 - (Number taking Both) + 3

Then, we solve for the number taking both subjects:

25 = 35 - (Number taking Both) + 3

25 = 38 - (Number taking Both)

(Number taking Both) = 38 - 25

(Number taking Both) = 13

Therefore, 13 class members take both history and geography.