2.3 Combination Problems

Ex 1 An artist has an apple, an orange, and a pear in his refrigerator. In how many ways can the artist choose one or more pieces of fruit for a still-life painting?

Ex 2 In how many ways can the student’s council executive (10 students) form a dance committee of at least 3 students?

A set with n distinct elements has subsets. You will have to decide if you need to subtract anything due to exclusion.

Ex 3 In an office break room, a special order form must be filled out if they require more than 3 cases of cookies, 4 cases of soft drinks, and 2 cases of coffee. How many ways can they stock the break room without requiring a special order form?

Combinations with alike items: where you have p alike items of one type, q alike items of a second type, r alike items of a third type, etc.

Ex 4 20 people are taking a tour in a double decker bus. 4 passengers refuse to travel outside and 5 refuse to travel inside, in how many ways can the passengers be seated with respect to inside/outside?

Problem solving method for Permutations/Combinations:

Is order important?

Yes: Use permutations Can the same objects be selected more than once? Yes: Fundamental Counting Principal No: Are some of the objects identical? Yes: Use No: Use

No: Use combinations Are you choosing exactly r objects? Yes: Could some of the objects be identical? Yes: Count the cases No: Use No: Are some of the objects identical? Yes: Use No: Use

p.286#1-13