**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. **

**Randomly choose 4 with replacement****Choose 4 one by one without replacement****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 **

**begins with a consonant****ends with a vowel****has the consonant and vowels alternating**