Section 10.5 and 10.6

I will be at a CS Education conference Wednesday and today. In order to keep you moving forward I have prepared the following materials to give you some practice opportunities with video explanations from me if you are having troubles.

Before you begin, make sure you have read sections 10.5 and 10.6 in your textbook.

 

Activity 1

Let's review permutations

  1. How many different ways can 10 flavors of ice cream be arranged in an ice cream store display case?
  2. How many different ways are there arrange 6 candidate names on a ballot?
  3. How many permutations of the characters in COMPUTER are there?
  4. How many of the permutations from problem #3 end in a vowel?
  5. How many ways can 6 people be seated in a circle of 6 chairs? Only relative positions in the circle can be distinguished.
  6. In how many ways can first, second, and third prize in a pie-baking contest be given to 15 contestants?
  7. Stock designations on the stock exchange are limited to 3 letters. How many different designations are there?
  8. How many different stock designations are there if letters cannot be repeated?
  9. In how many ways can 19 people be seated in a row?
  10. In how many ways can 11 men and 8 women be seated in a row?
  11. In how many different ways can 11 men and 8 women be seated in a row if the men all sit together and the women all sit together?

 

 

Combinations

The way your book names this material is weird. I want to talk about that and revisit some material.

 

Activity 2

Calculate the value of:

  1. C(7,3)
  2. C(10,5)
  3. C(6,5)
  4. C(6,6)
  5. C(n,3)
  6. C(n,n-3)

 

Activity 3

Consider the following

  1. Quality control wants to test 25 microprocessor chips from the 300 manufactured each day. How many different batches of test chips are possible?
  2. A soccer team carries 18 players on the roster; 11 players make the starting line up. How many different starting lineups are possible?
  3. How many juries of 5 men and 7 women can be formed from a panel of 17 men and 23 women?
  4. How many different sets of 4 novels and 3 plays can be assigned in an English class from an approved list of 21 novels and 11 plays?

 

Activity 4

Of a company's personnel, 7 people work in design, 14 in manufacturing, 4 in testing, 5 in sales, 2 in accounting and 3 in marketing. A committee of 6 people is to be formed to meet with upper management.

  1. How many committees are possible?
  2. How many committees with 1 member from each department are possible?
  3. How many committees with no members of manufacturing are possible?
  4. How many committees with exactly 2 members from manufacturing are possible?
  5. How many committees with no representative from accounting and exactly 1 member from marketing are possible?