5. In another state, license plates are formed using 6 symbols, any of which can be a number or a letter. a) How many license plates are there? b) What is the probability that a license plate has the following? I. All letters. II. At least one letter. III. At least 5 numbers. ^ IV. An even number first, a multiple of 3 second, a consonant third, a vowel fourth, and anything at all fifth and sixth. In with booh
5. In another state, license plates are formed using 6 symbols, any of which can be a number or a letter. a) How many license plates are there? b) What is the probability that a license plate has the following? I. All letters. II. At least one letter. III. At least 5 numbers. ^ IV. An even number first, a multiple of 3 second, a consonant third, a vowel fourth, and anything at all fifth and sixth. In with booh
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
For question 5b)IV)
The answer is
(5 x 3 x 21 x 5 x 36^2) / 36^6
Why does the answer not include combinations?
For example why does it not start with
10C5 instead?
![5. In another state, license plates are formed using 6 symbols, any of which can be a number or a
letter.
a) How many license plates are there?
b) What is the probability that a license plate has the following?
I. All letters.
II. At least one letter.
III. At least 5 numbers.
in with
^
IV. An even number first, a multiple of 3 second, a consonant third, a vowel fourth, and h
anything at all fifth and sixth.
6. Given a standard deck of cards. What is the probability the top card is:
a) a black ace?
b) not a black ace?
c) a diamond face card?
d) a jack or a king?
e) neither a queen nor an ace?
7. In drawing 5 cards from a standard deck of cards without feplacement, what is the
probability of:
combination
a) getting 5 spades?
b) getting 5 black cards?
4
c) getting 5 face cards?
12
4
d) getting just face cards or aces?
e) getting 4 aces?
f) getting 2 aces and 3 queens?
is 32+
52
8. The board of regents of a university is made up of 12 men and 16 women. If a committee
is chosen at random, what is the probability:
a) that it will contain 3 men and 3 women?
b) that it will contain 4 men and 2 women?
9. A town council consists of 8 Democrats, 7 Republicans, and 5 Independents. A committee
of 3 is chosen by randomly pulling names from a hat. What is the probability that the
committee has:
a) 2 Democrats and 1 Republican?
b) 3 Independents?
X25
c) no Independents?
24 23
d) 1 Democrat, 1 Republican, and 1 Independent?
e) at least one Independent?
10. Each of five cards is labeled with a letter A, B, C, D, or E. Two cards are chosen at random
without replacement. Find the probability that:
a) both letters chosen are consonants.
b) both letters chosen are vowels.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbad1c991-07cd-414d-a37c-f7238c094fb9%2Ff6db1833-3f8e-4cbc-80e8-039aeb72d8ed%2F8nwxwx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. In another state, license plates are formed using 6 symbols, any of which can be a number or a
letter.
a) How many license plates are there?
b) What is the probability that a license plate has the following?
I. All letters.
II. At least one letter.
III. At least 5 numbers.
in with
^
IV. An even number first, a multiple of 3 second, a consonant third, a vowel fourth, and h
anything at all fifth and sixth.
6. Given a standard deck of cards. What is the probability the top card is:
a) a black ace?
b) not a black ace?
c) a diamond face card?
d) a jack or a king?
e) neither a queen nor an ace?
7. In drawing 5 cards from a standard deck of cards without feplacement, what is the
probability of:
combination
a) getting 5 spades?
b) getting 5 black cards?
4
c) getting 5 face cards?
12
4
d) getting just face cards or aces?
e) getting 4 aces?
f) getting 2 aces and 3 queens?
is 32+
52
8. The board of regents of a university is made up of 12 men and 16 women. If a committee
is chosen at random, what is the probability:
a) that it will contain 3 men and 3 women?
b) that it will contain 4 men and 2 women?
9. A town council consists of 8 Democrats, 7 Republicans, and 5 Independents. A committee
of 3 is chosen by randomly pulling names from a hat. What is the probability that the
committee has:
a) 2 Democrats and 1 Republican?
b) 3 Independents?
X25
c) no Independents?
24 23
d) 1 Democrat, 1 Republican, and 1 Independent?
e) at least one Independent?
10. Each of five cards is labeled with a letter A, B, C, D, or E. Two cards are chosen at random
without replacement. Find the probability that:
a) both letters chosen are consonants.
b) both letters chosen are vowels.
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