Question

An English examination has two sections. Section A has five questions and section B has four questions, Four questions must be answered in total.

how many different ways are there of selecting four questions if there must be at least one question answered from each section?

Answer 1

To calculate the total number of ways of selecting four questions, we first find the total number of ways of selecting four questions without any restrictions. This is the number of ways of selecting four questions from the nine available, which is 9C4 = 126.

Next, we find the number of ways of selecting four questions if none are selected from section A or none are selected from section B. The number of ways of selecting four questions from section A is 5C4 = 5, and the number of ways of selecting four questions from section B is 4C4 = 1. So the total number of ways of selecting four questions if none are selected from section A or section B is 5 + 1 = 6.

Finally, we subtract the number of ways of selecting four questions if none are selected from either section from the total number of ways of selecting four questions to get the number of ways of selecting four questions if at least one question is selected from each section: 126 - 6 = 120.

Therefore, there are 120 different ways of selecting four questions if there must be at least one question answered from each section.