Question

A teacher is creating a quiz for her class. Each student's quiz will contain the same set of questions, but every student's questions will appear in a different order. If there are thirty students in the class, what is the least number of questions the quiz can contain

Answer 1

Answer:

5

Step-by-step explanation:

The test can be arranged in n! ways

If there is 1 question, the question can be arranged in 1! way = 1

If there are 2 question, the question can be arranged in 2! ways = 2 x 1 = 2

If there are 3 question, the question can be arranged in 3! ways = 3 x2 x 1 = 6

If there are 4 questions, the question can be arranged in 4! ways = 4 x 3 x2 x 1 = 24

If there are 5 questions, the question can be arranged in 5! ways = 5 x 4 x 3 x2 x 1 = 120 ways

the  least number of questions the quiz can contain is 5 because it is the number that yields the number of arrangements that is greater than 30