Find the number of ways in which a French test can be made.
20 questions from a test bank of 100 questions
The first question one has 100 choices, then the second question 99 choices, then the third 98 choices....see the pattern?
To find the number of ways in which a French test can be made, we can use the concept of combinations.
In this case, we want to select 20 questions from a test bank of 100 questions.
The formula to find the number of combinations is:
C(n, r) = n! / (r!(n-r)!)
Here, n is the total number of items (100 questions) and r is the number of items being selected (20 questions).
Using the formula, we can calculate the number of ways:
C(100, 20) = 100! / (20!(100-20)!)
= 100! / (20! * 80!)
≈ 535983370403809682970
Therefore, there are approximately 535,983,370,403,809,682,970 ways in which a French test can be made.
To find the number of ways in which a French test can be made with 20 questions from a test bank of 100 questions, you can use the concept of combinations.
The formula for combinations can be represented as:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items to choose from (100 questions in this case) and r is the number of items to be chosen (20 questions in this case), and "!" denotes factorial.
Using this formula, we can calculate the number of combinations.
C(100, 20) = 100! / (20!(100-20)!)
To simplify calculations, we can cancel out common terms:
C(100, 20) = (100 * 99 * 98 * ... * 81 * 80!) / (20 * 19 * 18 * ... * 3 * 2 * 1)
Now we can calculate the value using a calculator or a mathematical software:
C(100, 20) ≈ 535983370403809682970
Therefore, there are approximately 5.36 x 10^20 ways in which a French test can be made with 20 questions from a test bank of 100 questions.