In a class of 180 students 95 passed in History, 38 failed in Geography.  73 passed in both. How many students failed in at least one subject?

To solve this problem, we need to find out how many students passed both subjects, how many passed only one subject, and how many failed both subjects.

Step 1: Find out how many students passed both subjects. The problem states that 73 students passed both History and Geography.

Step 2: Find out how many students passed only one subject. The problem states that 95 students passed History and 38 students failed Geography. This means that 95 - 73 = 22 students passed only History. Similarly, since the total number of students is 180 and 38 students failed Geography, this means that 180 - 38 = 142 students passed Geography. But we know that 73 of these also passed History, so 142 - 73 = 69 students passed only Geography.

Step 3: Find out how many students failed both subjects. We know that 22 students passed only History, 69 students passed only Geography, and 73 students passed both subjects. This means that 22 + 69 + 73 = 164 students passed at least one subject. Since the total number of students is 180, this means that 180 - 164 = 16 students failed both subjects.

Step 4: Find out how many students failed at least one subject. We know that 22 students passed only History, 69 students passed only Geography, and 16 students failed both subjects. This means that 22 + 69 + 16 = 107 students failed at least one subject.

So, 107 students failed in at least one subject.