Applications of permutations and introduction to combinations.

1. Richard

2. Vincent

3. Sandy

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

6. 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)

7. 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)

8. (a) In how many ways can the letters of the word GEOMETRY be arranged
so that vowels and consonants alternate?
(b) In how many of these ways is Y the last letter?

9. (a) In how many ways can the letters of the word GEOMETRY be arranged
so that vowels and consonants alternate?
(b) In how many of these ways is Y the last letter?

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

11. Combination: An arrangement of objects where order does not matter.
Formula: A.K.A the "Choose" formula.
n is the number of objects to choose from
r 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?
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