How many different possible tests consisting of 18 questions can be made from a test bank of 20 questions

Answer 1

The number of ways to choose 18 questions from a pool of 20 is given by the combination formula:

C(n, k) = n! / (k!(n-k)!)

where:
n = total number of items in the pool (20 questions)
k = number of items to be chosen (18 questions)

Plugging in the values:
C(20, 18) = 20! / (18!(20-18)!)
C(20, 18) = 20! / (18!2!)
C(20, 18) = (20 × 19 × 18!) / (18!2)
C(20, 18) = 20 × 19 / 2
C(20, 18) = 190

Therefore, there are 190 different possible tests consisting of 18 questions that can be made from a test bank of 20 questions.