Seating assignments are an excellent format for permutation math problems because the location of each student in the classroom is significant in the problem. Figuring out how many different seating assignments there can be for a class of n seats is a simple permutation problem (the answer is n! or "n factorial"). A class of 8 students has 8! possible seating arrangements, or 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.
For more challenging problems, add more requirements, such as a seating assignment that alternates boys and girls for a class that is 50% boys and 50% girls (the answer is 2 x 4! x 4! = 1152 possible arrangements).
Tournament seeding is another type of word problem in which order matters, so you must use permutations to determine the total number of possible tournament groupings. A tournament with n seeds has n! number of possible groupings. A more challenging problem is to determine the number of possible 16-seed groupings when the number of teams to qualify for the tournament is more than 16. For this calculation, you would need to find the value of P(n,16), where n is the number of teams before qualification. The formula for P(n,16) is n!/(n - 16)!.
Card games with the standard 52-card, four-suited deck present dozens of opportunities for combination math problems. A classic example is determining the number of different ways you can be dealt a certain poker hand. The number of ways to get three of a kind in a five-card hand is 78 = 13 x C(4,3) -- which is equal to 4! / 3! -- because C(4,3) represents the number of ways to get three of a kind of a certain card and there are 13 different cards in a deck. Ask students if they can come up with formulas to determine the number of possible ways to get other hands.
Team selection is another combination math problem; find the number of possible n-player teams from a p-player roster. The formula to find the answer is C(n,p), or n! / (p! * (n - p)!). As always, you can make the problems more challenging by adding additional parameters. For example, the formula for the number of possible n-player teams with a unique team captain is C(n,p) multiplied by n because there are n different captain choices for each team.