Divide students up into groups of three or four. Tell them that their families are ordering a large submarine sandwich and of four different possible fillings--say ham, cheese, lettuce and tomato--they can only pick three for their sandwich. Give each group little pieces of construction paper with H, C, L and T on them to serve as a visual aid. Give each group time to determine how many possible sandwich combinations they could order, then when the time is up, have them explain how they got their answer. Use this is a segue to a lesson on combinations.
Once students have made and discussed their sandwich combinations, have them go back and determine how many arrangements of their sandwich toppings they could make. For example, if they made a sandwich with cheese, lettuce and tomato, that could alternately be cheese, tomato and lettuce; tomato, cheese and lettuce; tomato, lettuce and cheese; lettuce, cheese and tomato and lettuce, tomato and cheese. Once again, give the groups time to discuss and explore on their own then have them present their findings and methods to the class. Use this as a segue into a lesson on permutations.
For students already acquainted with the concepts of permutations and combinations, break them up into groups of three or four and divide a stack of playing cards randomly through the group. Have each group arrange the cards into as many different combinations and permutations as they can based on changing qualities. For example, first have them find combinations and permutations based on card color, then number, suite, then face card or number card. Have a prize ready for the group or groups that most consistently find all the results.
Have students brainstorm real-life situations in which they have, or will likely need to, work with permutations and combinations. Examples might include planning seating for a banquet, combinations of pills or toppings on a sundae. Have the students explain whether their scenarios represent combinations or permutations and have them calculate how many possible different combinations or permutations of each situation there are.