Choose three marbles.How many ways can you do that?

Combinations

marbles

Swirly Marbles @ Moon Marbles, Bonner Springs, KS

How many different necklaces can be made from 12 beads of different colours?

Mom and dad and their 6 children (3 boys and 3 girls) are to be seated at a circular table. How many ways can this be done if mom and dad sit together and the males and females alternate?

In how many ways can the student council choose a subcommittee of 5 people from the entire council which consists of 11 people?

Number of 49 letter wordsmade up of 6 Y's and 43 N's

Solution as a CombinationSolution by a Permutation of Non-Distinguishable Objects

Example: How many different tickets can be sold in the 6/49 lottery?

A.K.A the "Choose" formula.

n is the number of objects to choose fromr is the number of objects to be arranged is read as "n choose r" means: Given a set of n objects, how many different groups of n objects can be chosen where order does not matter?

Formula:

Combination: An arrangement of objects where order does not matter.

QUIZ

Pizza Hut offers 3 choices of salad, 20 kinds of pizza, and 4 different desserts. How many different 3-course meals can one order?

(a) the president is to be female and the secretary male? (2 marks)

(b) the president is to be male and the secretary female? (2 marks)

(c) the president and secretary are to be of opposite sex? (1 mark)

Suppose that the DMCI subcommittee of for the study of Flibberdejibbets consists of 3 girls and 2 boys. In how many ways can a president and secretary be chosen if:

There are five main roads between the cities A and B, and four between B and C. In how many ways can a person drive from A to C and return, going through B on both trips, without driving on the same road twice? (2 marks)

In how many ways can 8 books be arranged on a shelf, if 3 particular books must be together?

How many different necklaces of 12 beads each can be made from 18 beads of different colours?