# Activities to Teach Students Permutation and Combination Notation

Permutation and combination notation are two fundamental concepts in combinatorics, a branch of mathematics that concerns itself with counting and ordering objects. Students often find these concepts challenging as they require a new way of thinking and reasoning. Fortunately, several activities can make learning permutation and combination notation easier and more fun.

Here are some engaging activities to teach students permutation and combination notation:

1. Bookshelf activities:

Start by asking students to arrange books on a bookshelf in different ways. For example, how many ways can books be arranged on a shelf with five spaces? Have students use the permutation formula nPr = n! / (n-r)! to calculate the number of permutations possible.

2. Pizza toppings activity:

Give students different pizza toppings and ask them to create different types of pizzas. For example, a pizza with two toppings, a pizza with three toppings, and so on. Ask them to use the combination formula nCr = n! / (r! × (n-r)!) to calculate the number of combinations possible.

3. Card games:

Permutation and combination notation can also be taught through card games like poker and rummy. Students can calculate the number of possible hands that can be dealt using the permutation or combination formula.

4. Dice games:

Similar to card games, dice games can also be used to teach permutation and combination notation. For example, ask students to calculate the number of possible outcomes when rolling two dice or three dice.

5. Scavenger hunt:

Create a scavenger hunt where students need to find objects with a specific combination of attributes. For example, they may need to find objects that are red, square, and small. This activity helps students understand how the order of attributes does not matter in combination notation.

6. Creative writing activity:

Ask students to write a story in which the order of events matters. For example, they may write about a day in the life of a superhero and the order in which they use their powers. This activity can help students understand the importance of permutation in storytelling.

In conclusion, permutation and combination notation are essential concepts in combinatorics that can be challenging for students to grasp. However, by using engaging activities like those described above, teachers can make learning these concepts easier and more fun for their students. By understanding permutation and combination notation, students develop critical thinking and problem-solving skills that can benefit them for the rest of their lives.