Combinations, a quiz on the fundamental principle of counting and some more practice problems.

1. Swirly Marbles @ Moon Marbles,
Bonner Springs, KS
Combinations
Choose three marbles.
marbles
How many ways can you do that?

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

3. 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?

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

6. Combination: An arrangement of objects where order does not matter.
Formula: A.K.A the quot;Choosequot; formula.
n is the number of objects to choose from
r is the number of objects to be arranged
is read as quot;n choose rquot;
means: Given a set of n objects, how many different groups of n
objects can be chosen where order does not matter?
Example: How many different tickets can be sold in the 6/49 lottery?
Solution by a Permutation of Solution as a Combination
Non-Distinguishable Objects
Number of 49 letter words
made up of 6 Y's and 43 N's

7. QUIZ

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

10. 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:
(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)

11. 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)

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

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