Combination Activity 1

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Objectives

Students will be able to calculate a combination using a formula.

Students will have an understanding of what a combination is.

Students understand the difference between permutations and combinations

Estimated Time

Prerequisites/Instructions, prior preparations, if any

Materials/ Resources needed

Counting Sticks (Match sticks), Paper, Pencil

Process (How to do the activity)

Problem


Say, three people are eligible to win two similar prizes.


Method


Now the students can reason this out. Three people are eligible to win two prizes. Both prizes are exactly the same. Break out the counting sticks and see what the students come up with for this combination.


Win Prize 1 (W) Win Prize 2 (W) Loss (LS)




Shariff


W


W


W


LS


W


LS


Ashwini


W


LS


W


W


LS


W


Rakesh


LS


W


LS


W


W


W


Students should notice that columns are repeating when the prize is similar and hence there are only 3 outcomes. Students will be told this is the way “choose” as it is sometimes called, to pick or unordered outcomes from n possibilities. Stress the unordered part.

Extend this problem by asking the students how 20 people can win 5 prizes. This will be difficult to do manually and hence the formula will need to be used.

Evaluation at the end of the activity

Student tries to solve the following problem.

First tries it in a table with classroom of 3 students and 2 students needing to stay back after school and then uses the formula.

In a classroom filled with 20 students, 2 will be selected to stay after school and help their teacher for a programme.How many combinations are possible?

Answer : 190