d) Consider the weighted voting system [34: 10, 10, 10, 10, w]. Find all positive integers w which makes P5 a dummy. Enter your answers in ascending order separated by commas but not spaces. w=

If the chair of a math department has to appoint a committee of 4 professors from among the 10 professors in the department, how many different possibilities are there for the composition of the committee?

An election has 5 candidates. How many rankings of candidates are possible.

eight cars are in a race. there will be first place, second place and third place winners. assuming no ties, how many possible results are there for this race?

There are 25 applicants for four jobs; Computer Programmer, Software Tester, Manager, and Systems Engineer. This is an example of [Select] n= [Select] r = [Select] There are [Select] ways to choose an applicant for the positions of a computer programmer, software tester, manager, and systems engineer.