Math 30-2

Unit 2: Counting Methods

Lesson 7: Problem Solving With Permutations and Combinations

5. Fifteen students have been elected to be on student's council.

a) In how many ways can 5 of these students be chosen to be on the Mayor's Advisory

Committee on Youth?

b) In how many ways can a present, vice-president, secretary and treasurer be chosen from

the fifteen students?

c) Eight of the fifteen students elected are girls. In how many different orders can six of

the students line up for a picture if there must be an equal number of boys and girls in the

photograph?

6. A town in rural Alberta has 8 streets running north to south and 5 avenues running east to

west. The letter carrier has to carry letters from the extreme north-west intersection to the

extreme south-east intersection, only moving south or east along the streets and avenues.

Jim used the expression 13!/8!5! to determine the number of different ways to go from the

extreme north-west intersection to the extreme south-east intersection. Draw a diagram to

illustrate the situation and explain why Jim was incorrect in his reasoning.

7. How many arrangements are there of the letters of the word ATTAINTMENTS under each

condition?

a) without restrictions. b) if each arrangement begins with an M.

c) if each arrangement begins with T. d) if the T's are to be together.

8. A window display is being made for Halloween. There are eight black items and seven

orange items. Five items are being chosen for the window. The display is to have three

orange items and two black items arranged all in one row. Determine the number of

displays that can be made by choosing the items first and then arranging them in the

window.

9. For a certain type of computer chips are used that have five, six or seven circuits on them.

There are two different types of coded circuits on the chips. They are coded A or B. For

example a five circuit chip could have the code AAABB, where it has three of the type A

circuit and two of the type B circuit. How many different types of chips are available to

build the computer?

10. How many arrangements of the letters of the word PARALLELOGRAM, in which all the

L's are together at the end of the arrangement, are there?