Examples for Section 2.3 : Counting Techniques

Example1: A house owner doing some remodelling requires the services of both a plumbing contractor and an electrical contractor; there are 12 plumbing contractors and 9 electrical contractors, in how many ways can the contractors be chosen?

Example 2: A family requires the services of both an obstetrician and a pediatricion. There are two accessible clinics, each having two obstetricians and three pediatricions, family needs to select both doctor in the same clinic, in how many ways this can be done?

Example3: There are 8 TA's are available, 4 questions need to be marked. How many ways for Prof. To choose 1 TA for each question? How many ways if there are 8 questions?

Example 4: In a box, there are 10 tennis balls labeled number 1 to 10.

  1. Randomly choose 4 with replacement

  2. Choose 4 one by one without replacement

  3. grab 4 balls in one time

What is the probability that the ball labelled as number 1 is chosen?

Example 5: A rental car service facility has 10 foreign cars and 15 domestic cars waiting to be serviced on a particular Sat. morning. Mechanics can only work on 6 of them. If 6 were chosen randomly, what's the probabilty that 3 are domestic 3 are foreign? What's the probabilty that at least 3 domestic cars are chosen?

Example 6: If a permutation of the word “white” is slelcted at random, find the probability that the permutation

  1. begins with a consonant

  2. ends with a vowel

  3. has the consonant and vowels alternating