In a class of 25 members, 15 offer history, 17 offer geography and 3 offer neither of the subject. How many members offer both subject.
remember your inclusion-exclusion rules.
15+17-x = 25-3
x = 10
To find out how many members offer both history and geography, we will first calculate the total number of students who offer either history or geography.
Total students who offer history = 15
Total students who offer geography = 17
Now, we need to find the total number of students who offer either history or geography by adding both numbers:
Total students who offer either history or geography = 15 + 17 = 32
But we need to subtract 3 from this total as 3 students offer neither subject.
Total students who offer history or geography, including both = 32 - 3 = 29
Therefore, the number of members who offer both history and geography subjects is 29.
To find the number of members who offer both history and geography, we can use the principle of inclusion-exclusion.
First, we know that there are 15 members who offer history, 17 members who offer geography, and 3 members who offer neither subject. However, we don't know how many members offer both subjects yet.
Let's start by finding the total number of students who offer either history or geography. We can do this by adding the number of members who offer history (15) and the number of members who offer geography (17):
15 + 17 = 32
But this count includes some students who offer both history and geography, so we need to subtract the number of students who offer both subjects from this total.
Let's assume that there are 'x' members who offer both history and geography. We can now modify our equation:
15 + 17 - x = 32
Now we can solve for 'x':
x = 15 + 17 - 32
x = 32 - 32
x = 0
From this calculation, we find that there are 0 members who offer both history and geography.