If there are four judges and three contenders in a show choir competition, and each judge shall choose only one winner, in how many ways can the judges cast their votes?

As a fundraiser, a local GAA club runs a lotto-type draw in which 4 numbers are drawn from 20. As well as paying out a prize for a ticket with all four winning numbers, the club also refunds the price of any ticket which has none of the winning numbers. How many different tickets are there, and how many of them will have none of the four winning numbers? b) At the end of each season, two soccer leagues have an inter-league knock-out tournament between the top 4 teams in each league - in which the winners of each league play the 4th team in the other and the runners-up play the 3 team from the other league. If one league has 10 teams and the other league has 12 teams, how many different possible quarter-final line-ups are there?

There are six men and seven women in a ballroom dancing class. If four men and four women are chosen and paired off, how many pairings are possible?

The University of Ballygobackwards has three colleges: the College of Science, which has 15 staff, 5 of whom are female; the College of Engineering, which has 8 staff, 4 of whom are female; and the College of Arts, which has 17 staff, 6 of whom are female.   Each college has a Dean, who is chosen from the staff in that college.   What is the total number of ways these three Deans can be chosen? Answer:   How many ways can three Deans be chosen, so that at least one of them is female? Answer: