How many ways can you answer 5 true false questions? This is a question that might seem simple at first glance, but upon closer inspection, it reveals a fascinating mathematical concept. In this article, we will explore the different ways to answer a set of five true false questions and understand the underlying mathematics behind it.
In a true false question, there are only two possible answers: true or false. Therefore, for each question, there are two choices. When it comes to answering five true false questions, we can use the concept of combinations to determine the number of possible ways to answer them.
To calculate the number of ways to answer five true false questions, we can use the formula for combinations, which is given by:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of questions, k is the number of questions we want to answer, and “!” denotes the factorial of a number.
In our case, n = 5 (since there are five questions) and k = 2 (since each question has two possible answers: true or false). Plugging these values into the formula, we get:
C(5, 2) = 5! / (2!(5-2)!)
C(5, 2) = (5 × 4 × 3 × 2 × 1) / (2 × 1 × 3 × 2 × 1)
C(5, 2) = 120 / 12
C(5, 2) = 10
So, there are 10 different ways to answer five true false questions. These ways include all possible combinations of true and false answers for the five questions.
Let’s list some of these combinations:
1. True, True, True, True, True
2. True, True, True, True, False
3. True, True, True, False, True
4. True, True, True, False, False
5. True, True, False, True, True
6. True, True, False, True, False
7. True, True, False, False, True
8. True, True, False, False, False
9. True, False, True, True, True
10. True, False, True, True, False
As we can see, each combination represents a unique way to answer the five true false questions. The number of combinations grows exponentially as the number of questions increases. For example, if we had 10 true false questions, there would be 2^10 = 1024 different ways to answer them.
In conclusion, the answer to the question “How many ways can you answer 5 true false questions?” is 10. This simple question demonstrates the power of combinations and factorial calculations in mathematics, and it highlights the vast number of possibilities that arise from seemingly straightforward choices.
