Question

68) Six problems were created with different versions. For problems 1, 3, and 4, the teacher 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.

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


d) If, in addition to the different versions for each problem, the teacher decides to place the problems in random order, how many different exams are possible?

Answer 1

c) Number of different tests that can be done if each test will have a version of each problem is computed here as:
= Num of versions of first problem * Num of versions of second problem * ..... Num of version of the the last problem

= 5³*4²*1

= 2000

therefore there are 2000 different tests possible here.

d) As the order of the problems is also important here, the number of different tests is computed here as:

= Number of different tests possible using different versions of 6 problems * Number of permutation of 6 problems chosen

= 2000*6!

= 1440000

Therefore there are 1440000 different tests possible here.