Question

date:

1. background assumptions concerning florida license plates:

• license plates have 7 characters
• the first 3 characters have to be numbers
• the next 3 characters have to be letters
• the very last character can be a letter or the numbers 0 or 1
• in addition, the very first character cannot be the number 9 as those are assigned to government vehicles

using this information, how many license plates can be distributed in florida?

1. background assumptions concerning texas license plates:

• license plates have 7 characters
• the first 4 characters have to be letters
• the last 3 characters have to be numbers
• the last number cannot be a 9 or 1
• the first and second letter cannot be a vowel (multiple correct answers)

using this information, how many different license plates can be distributed?

1. all 5 - digit zip codes in the united states are assigned by region. in north dakota, the first digit can be a 4 or a 9. the second, third and fourth digits can be any odd number between 0 and 9. the last digit must be an even number between 0 and 9. how many zip codes are possible?

1. a new concert venue just opened in downtown atlanta and they are in the process of deciding how many tickets they can sell for each show. the venue has three levels, two general admission that only have standing room, and one level with 150 seats. the first level of standing room is a square with one side measuring 75 ft. the second level, also standing room, is a rectangle measuring 100 ft. by 50 ft. the third level has 150 seats. the venue thinks each person will occupy 2.25 square feet. how many tickets should they sell?

Explanation:

Question 11

Step1: Determine options for first character

The first character is a number (0 - 8, since 9 is excluded), so 9 options.

Step2: Determine options for second and third characters

Each of the second and third characters is a number (0 - 9), so 10 options each.

Step3: Determine options for fourth, fifth, and sixth characters

Each of these is a letter (26 letters), so 26 options each.

Step4: Determine options for seventh character

The seventh character can be a letter (26) or 0/1 (2 numbers), so 26 + 2 = 28 options.

Step5: Calculate total number of license plates

Multiply the number of options for each character: \(9\times10\times10\times26\times26\times26\times28\)
First, calculate \(9\times10\times10 = 900\)
Then, \(26\times26\times26 = 17576\)
Then, \(900\times17576 = 15818400\)
Then, \(15818400\times28 = 442915200\)

Step1: Determine options for first and second letters

Vowels are a, e, i, o, u (5 vowels), so consonants are 26 - 5 = 21. First and second letters: 21 options each.

Step2: Determine options for third and fourth letters

Each is a letter (26 options each).

Step3: Determine options for fifth and sixth characters

Each is a number (0 - 9, 10 options each).

Step4: Determine options for seventh character

Seventh character is a number (excluding 9 and 1, so 8 options: 0,2,3,4,5,6,7,8).

Step5: Calculate total number of license plates

Multiply the number of options: \(21\times21\times26\times26\times10\times10\times8\)
First, \(21\times21 = 441\)
\(26\times26 = 676\)
\(10\times10 = 100\)
Then, \(441\times676 = 298116\)
\(298116\times100 = 29811600\)
\(29811600\times8 = 238492800\)

Step1: Determine options for first digit

First digit: 4 or 9, so 2 options.

Step2: Determine options for second, third, and fourth digits

Each is an odd number (1,3,5,7,9), so 5 options each.

Step3: Determine options for fifth digit

Fifth digit is even (0,2,4,6,8), so 5 options.

Step4: Calculate total number of zip codes

Multiply the number of options: \(2\times5\times5\times5\times5\)
First, \(5\times5\times5\times5 = 625\)
Then, \(2\times625 = 1250\)

Answer:

442915200

Question 12