# Finance Homework Help

Posted by:**admin**| Posted on:

**November 23, 2014**

Focus Set 3 – Fundamental Counting Principle

Provide answers to # 1 – 10 below.

Show how you set up your problem and then do the math.

1. If there are four roads from town A to town B and three roads from town B to town C, how many routes are there from town A to town C which go through town B?

Number of routes from A to C

= Number of routes from A to B x Number of routes from B to C

= 4 x 3

= 12

2. How many different 4-letter radio station call codes are possible if each code must begin with K or W and no letter can be repeated? Examples: WABC, KABC, or WABK

Number of call codes possible

= Product of number of choice of each digit

= 2 x 25 x 24 x 23

= 27600

3. A firm wants to assign its employees ID numbers that have say x digits each. If a firm has 800 employees, what is the smallest number of digits (that is, the smallest x) that the firm can use for each ID number? Assume that repetition of digits is permitted.

(Hint: There is no formula for this – you just have to reason it out, but you must be enough ID’s to go around!)

For x number of digits, number of distinct ID = 10x

For x =2, number of distinct ID = 100 < 800 For x =3, number of distinct ID = 1000 > 800

Therefore the smallest x is 3

4. In how many ways can 10 questions on a True-False test be answered?

Number of ways

= 210

= 1024

5. In how many ways can a president and vice president be selected from a club consisting of 12 people?

(Assume that these 2 positions cannot be occupied by the same person.)

Number of ways

= Product of number of choice for each position

= 12 x 11

= 132

6. In how many ways can 5 people be seated in a row?

Number of ways for 5 people to sit in a row

= 5!

= 5 x 4 x 3 x 2 x 1

= 120

7. How many ways can 6 people be seated in a row, if Ruth must be seated in the first chair?

Since Ruth must sit in first chair, there are on one choice for first chair

Number of ways for remaining 5 people to sit in a row

= 5!

= 5 x 4 x 3 x 2 x 1

= 120

Total number of ways

= 1 x 120

= 120

8. How many distinct ordered arrangements can be made with the letters of the word TENNESSEE?

There are 4 repeated E, two repeated N, two repeated S, and totally 9 characters

Number of ways

=9!/(4!2!2!)

= 3780

9. You are trying to schedule classes for next semester and wish to enroll in Math, English, Fine Arts, and History. You have found 4 Math sections, 5 English sections, 6 Fine Arts sections, and 2 History sections that do not have conflicts.

How many different possible schedules can you develop using these options?

There are totally 4 + 5 + 6 + 2 = 17 sections

Number of ways

=17!/(4!5!6!2!)

= 85765680

10. It is lunchtime and you wish to build a pizza with 1 choice of crust, 1 meat, 1 vegetable.

You have the following choices: 2 types of crust, 4 types of meats, and 7 types of vegetables

How many different ways can you build your pizza?

Number of ways to build pizza

= Number of choice of crust x number of choice of meat x number of choice of vegetable

= 2 x 4 x 7

= 56

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