Question

The Mathematics Department of the University of Louisville consists of 8 professors, 6 associate professors, 13 assistant professors. In how many of all possible samples of size 4, chosen without replacement, will every type of professor be represented?

Answer 1

Answer:

16848

Step-by-step explanation:

Given that the Mathematics Department of the University of Louisville consists of 8 professors, 6 associate professors, 13 assistant professors.

When a sample of 4 is taken without replacement such that every type of profession is represented.

Hence no of ways to select this = selecting 1 from each from one group and then last one from any one of the total

No of ways = $8C1(6C1)(13C1)(8+6+13)C1\\= 8(6)(13) 27C1\\= 8(6)(13)(27)\\= 16848$