# Thread: The Fundamental Counting Principle

1. ## The Fundamental Counting Principle

The Fundamental Counting Princip le

1) In how many different ways can the letters of the word GREAT be rearranged if the new arrangement must begin with a T and repetitions are not allowed?

Is this right? 4! = 4 * 3 * 2 * 1 = 24

2) Some Ontario license plates have two letters followed by four digits. How many different license plates of this type are possible?

2. ## Re: The Fundamental Counting Principle

1.) Correct. You have 1 choice for the first letter, 4 for the second, 3 for the third, 2 for the fourth and 1 for the fifth. Thus, by the FCP the number of arrangements is:

$N=1\cdot4\cdot3\cdot2\cdot1=4!=24$

2.) If repetitions are allowed, how many choices do you have for each digit?

3. ## Re: The Fundamental Counting Principle

N = 2 * 1 = 2 n = 4 * 3 * 2 * 1 = 24
n = 26

4. ## Re: The Fundamental Counting Principle

2.) There are 26 letters of the alphabet to choose from for each of the first two digits, and 10 numeric digits to choose from for each of the last 4 digits. Hence:

$N=26\cdot26\cdot10\cdot10\cdot10\cdot10=26^2\cdot1 0^4=6760000$

5. ## Re: The Fundamental Counting Principle

one certainly hopes Ontario has fewer cars than that....