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, while 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 put the problems in random order, how many different tests are possible?

Answer 1

a) As the order of questions is not important here, we would be using the product rule here to find the number of different tests possible.

= Product of the different number of versions of each of the 6 problems

= 5³*4²*1

= 2000

Therefore there are 2000 different tests possible on the basis of choosing the different versions only.

b) Given that the order of questions is also important here, the number of different tests possible here is computed as:

= 2000* Number of permutations for those 6 questions chosen in part a)

= 2000*6!

= 1440000

Therefore there are 1440000 different tests that can be given here.