Question

Mr.Johnson doesn't want to make it easy for his students to cheat. He uses a 10 question problem bank to assign his students quiz questions. How many different 5 problem quizzes can he make if the order of questions is not considered?

Answer 1

To find the number of different 5 problem quizzes that Mr. Johnson can make from a 10-question problem bank, we can use the concept of combinations. The number of ways to select 5 questions out of 10 is 30,240.

Step-by-step explanation:

To find the number of different 5 problem quizzes that Mr. Johnson can make from a 10-question problem bank, we can use the concept of combinations. Since the order of the questions is not considered, we need to find the number of ways to select 5 questions out of 10. This can be calculated using the formula for combinations, which is nCr = n! / (r!(n-r)!). In this case, n = 10 (total number of questions) and r = 5 (number of questions to be selected). Plugging in these values, we get 10! / (5!(10-5)!), which simplifies to 10! / (5!5!).

10! (read as 10 factorial) means multiplying all the numbers from 10 down to 1. Similarly, 5! is the factorial of 5. We can cancel out the common factors of 5! in the numerator and denominator, resulting in 10 × 9 × 8 × 7 × 6. This calculates to 30,240 different 5 problem quizzes that Mr. Johnson can make.