Counting 2. In Ontario, commercial vehicle license plates currently have the format XX NNNNN, where XX are letters and NNNNN are numbers. A sample image is shown on the right. We are interested in how many license plates remain in this series. We assume that all license plate combinations in this format are eligible to be issued a license (i.e., no plates are skipped or left out for any reason). ONTARIO SEP AJ-42864 YOURS TO DISCOVER A sample Ontario Commercial License Plate (by Dvermeirre - CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curi d=42644451) a. How many total commercial license plate combinations are available in the format above? That is, how many total license plates can be formed for the above format, starting at AA 00000 and going to ZZ 99999? Give a short explanation for how you arrived at this quantity. b. Assume that all plates are released in order, so that AA 00000 is the first plate to be issued, then all plates of the form AA NNNNN (in numerical order) then AB 00000, then all plates of the form AB NNNNN, etc. For this part of the question, you are asked to use your initials to calculate how many license plates combinations remain after the plate XY N1337, where XY are your initials and N is the last digit in the date of your birthday. So, if you were born on the 13th of the month, the number N should be 3. If you were born on the 5th of the month, the number N should be 5. - For this question, choose a pair of initials that represents your name in some way. (So if you have three initials, pick two letters; if you have a name that you use that is different from your birth name, feel free to use that, etc.) - By "after" in this question, we mean that you should assume that the plate XY 01337 has been issued already, and the next plate to be issued is XY 01338. This is the first plate after XY 01337. For your initials and birth date digit, give the number of license plate combinations that come after XY N1337. Give the final number, plus an explanation of how it works, including breaking the quantity down into sections that illustrate how you arrived at your answer. Make sure to clearly indicate in your response your "personal" plate number that serves at the starting point - failure to do so will result in lost marks. If it is helpful, here's a table that shows the number of letters in the alphabet that are after a given letter. A B с D E F G H J 25 24 23 22 21 20 19 18 17 16 K L M N P Q R S T 15 14 13 12 11 10 9 8 7 6 U V W X Y Z 5 4 3 2 1 0

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
Problem 7T: An anagram of a word is a rearrangement of the letters of the word. (a) How many anagrams of the...
Question
Counting
2.
In Ontario, commercial vehicle license plates
currently have the format XX NNNNN, where XX are letters and
NNNNN are numbers. A sample image is shown on the right. We
are interested in how many license plates remain in this series.
We assume that all license plate combinations in this format are
eligible to be issued a license (i.e., no plates are skipped or left
out for any reason).
ONTARIO
SEP
AJ-42864
YOURS TO DISCOVER
A sample Ontario Commercial License Plate (by
Dvermeirre - CC BY-SA 4.0,
https://commons.wikimedia.org/w/index.php?curi
d=42644451)
a. How many total commercial license plate combinations are
available in the format above? That is, how many total license
plates can be formed for the above format, starting at AA 00000 and going to ZZ 99999? Give a short
explanation for how you arrived at this quantity.
b. Assume that all plates are released in order, so that AA 00000 is the first plate to be issued, then
all plates of the form AA NNNNN (in numerical order) then AB 00000, then all plates of the form AB
NNNNN, etc.
For this part of the question, you are asked to use your initials to calculate how many license plates
combinations remain after the plate XY N1337, where XY are your initials and N is the last digit in
the date of your birthday.
So, if you were born on the 13th of the month, the number N should be 3. If you were born on
the 5th of the month, the number N should be 5.
- For this question, choose a pair of initials that represents your name in some way. (So if you
have three initials, pick two letters; if you have a name that you use that is different from
your birth name, feel free to use that, etc.)
- By "after" in this question, we mean that you should assume that the plate XY 01337 has
been issued already, and the next plate to be issued is XY 01338. This is the first plate after
XY 01337.
For your initials and birth date digit, give the number of license plate combinations that come after
XY N1337. Give the final number, plus an explanation of how it works, including breaking the
quantity down into sections that illustrate how you arrived at your answer. Make sure to clearly
indicate in your response your "personal" plate number that serves at the starting point - failure to
do so will result in lost marks. If it is helpful, here's a table that shows the number of letters in the
alphabet that are after a given letter.
A
B
с
D
E
F
G
H
J
25
24
23
22
21
20
19
18
17
16
K
L
M
N
P
Q
R
S
T
15
14
13
12
11
10
9
8
7
6
U
V
W
X
Y
Z
5
4
3
2
1
0
Transcribed Image Text:Counting 2. In Ontario, commercial vehicle license plates currently have the format XX NNNNN, where XX are letters and NNNNN are numbers. A sample image is shown on the right. We are interested in how many license plates remain in this series. We assume that all license plate combinations in this format are eligible to be issued a license (i.e., no plates are skipped or left out for any reason). ONTARIO SEP AJ-42864 YOURS TO DISCOVER A sample Ontario Commercial License Plate (by Dvermeirre - CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curi d=42644451) a. How many total commercial license plate combinations are available in the format above? That is, how many total license plates can be formed for the above format, starting at AA 00000 and going to ZZ 99999? Give a short explanation for how you arrived at this quantity. b. Assume that all plates are released in order, so that AA 00000 is the first plate to be issued, then all plates of the form AA NNNNN (in numerical order) then AB 00000, then all plates of the form AB NNNNN, etc. For this part of the question, you are asked to use your initials to calculate how many license plates combinations remain after the plate XY N1337, where XY are your initials and N is the last digit in the date of your birthday. So, if you were born on the 13th of the month, the number N should be 3. If you were born on the 5th of the month, the number N should be 5. - For this question, choose a pair of initials that represents your name in some way. (So if you have three initials, pick two letters; if you have a name that you use that is different from your birth name, feel free to use that, etc.) - By "after" in this question, we mean that you should assume that the plate XY 01337 has been issued already, and the next plate to be issued is XY 01338. This is the first plate after XY 01337. For your initials and birth date digit, give the number of license plate combinations that come after XY N1337. Give the final number, plus an explanation of how it works, including breaking the quantity down into sections that illustrate how you arrived at your answer. Make sure to clearly indicate in your response your "personal" plate number that serves at the starting point - failure to do so will result in lost marks. If it is helpful, here's a table that shows the number of letters in the alphabet that are after a given letter. A B с D E F G H J 25 24 23 22 21 20 19 18 17 16 K L M N P Q R S T 15 14 13 12 11 10 9 8 7 6 U V W X Y Z 5 4 3 2 1 0
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