Unit 2 Combinations and The Binomial Theorem

2.1 Venn Diagrams

Venn Diagrams use circles to show how sets interact. The sets use circles and all the circles fit inside a rectangle.

Sets always take capital letters for their labels, and the elements inside them always take lower case letters.

The big box represents the universal set. It always takes the letter S for its label. S stands for ‘sample space’. Sample space refers to the context that the universal set reflects.

Ex 1 In my car, my radio presets include: 106.9 The Bear, 106.1 Chez, 93.9 Bob FM, Live 88.5, and 91.5 CBC. Use Venn Diagrams to illustrate the relationship between these radio stations.

Ex 2 There are 10 students on the volleyball team and 15 on the basketball team. When planning a field trip with both teams, the coach has to arrange transportation for a total of 19 students.

(a) What is the explanation for this?

(b) Illustrate this situation using a Venn diagrams.

(c) Determine how many students play for both teams.

Principle of Inclusion/Exclusion

or using set notation

Ex 2 Of the 140 grade 12 students at a high school:

• 52 signed up for biology
• 71 signed up for chemistry
• 40 signed up for physics
• 15 signed up for biology and chemistry
• 8 signed up for chemistry and physics
• 11 signed up for biology and physics
• 2 signed up for all 3.

(a) Determine how many students are not taking any science courses.

(b) Draw a Venn diagram.

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