Question

For a certain probability test, the teacher created 6 problems with different versions.
For problems 1, 3, and 4, he created five versions of each. For problems 5 and 6 there are
four versions of each, whereas for problem 2 there is only one version.

a. How many different tests can be done if each test will have a version of each
problem?

b. If in addition to the different versions for each problem, the teacher decides to place the
problems in random order, how many different tests are possible?

Answer 1

a) The number of possible tests in terms of combinations of different versions for each of the 6 questions is computed here as:

Using the product rule for the number of versions for each question as:

= 5³* 4² * 1

= 2000

Therefore there are 2000 different tests possible here.

b) As the order of questions is also important, therefore the total number of different tests possible is computed here as:

= 2000* Permutation of the 6 questions chosen

= 2000*6!

= 1440000

Therefore there are 1440000 possible different tests here.