mbers can 2. How many seating arrangements are possible be written using the following digits: 2,2,2,7,7,8,8,8, and 8? qPa = a! 312!4 721-2-1:43-2-1 * There are 1,260 different g-digit numbers that 3. A clothing store has a certain shirt in four can be wridten vsing the foil owing digis 4. In how many different ways can five keys, no two of which are the same, be arranged on a key-ring that has no clasp? P= (n-1)! = (5-1)! = 41= 24 = 12 for six people at a roundtable? P=Cn-1)= (6-1)! = 5! =120 * 7854321-1.260 There are 120 possible seat ing arrangements sizes: small, medium, large, and extra-large. If it has three small, four medium, four large, and two extra-large shirts in stock, in how many ways can these shirts be sold if each is sold one after the other? 13P13 There are 12 difterent ways thot S keys can be orranged 5. How many ways can nine people be seated at a roundtable relative to the door of a room? 9Pq - 9! 362,880 *There are 362, 880 ways 9 people can be seated on a roundtable. 7. What is the number of possible arrangements There are 12 ways"the girls and boys can of ten books on a shelf where four Algebra bt scated alternately books are of the same kind, three Geometry books are of the same kind, and three Statistics books are of the same kind? I0P10= 10 平313 = 6,227,029 800-600,600 TOT 368 There are 600,600 ways the shirts can be sdd 6. How many ways can three boys and three girls be seated alternately at a circular table? P= (n-1)! -(3-1)! = 2! 3! =\ 12 8. Eleven beads, no two of which are the same, are to be strung in a necklace with a clasp. In how many ways can it be done? P= n! = 11! = 39,916,800 =19a958,400 = 3,628,800 -14,200 864 2 *There, are 4,200 possible armangemants There are la,958,400 Ways the beads can be done. of the boolsS. 9. Find permutations of the digits of the number 843,838. GP6=61-20 =60 2121 * There are 60 distinguishable permutations There are 10 ways it can be arrang ed in a liind the number of distinguishable 10. Ana has two vases of the same kind and three candle stands of the same kind. In how many ways can shę arrange these items in a line? sPs- 51 5.4321-O 2! 2! 77 12T 12
mbers can 2. How many seating arrangements are possible be written using the following digits: 2,2,2,7,7,8,8,8, and 8? qPa = a! 312!4 721-2-1:43-2-1 * There are 1,260 different g-digit numbers that 3. A clothing store has a certain shirt in four can be wridten vsing the foil owing digis 4. In how many different ways can five keys, no two of which are the same, be arranged on a key-ring that has no clasp? P= (n-1)! = (5-1)! = 41= 24 = 12 for six people at a roundtable? P=Cn-1)= (6-1)! = 5! =120 * 7854321-1.260 There are 120 possible seat ing arrangements sizes: small, medium, large, and extra-large. If it has three small, four medium, four large, and two extra-large shirts in stock, in how many ways can these shirts be sold if each is sold one after the other? 13P13 There are 12 difterent ways thot S keys can be orranged 5. How many ways can nine people be seated at a roundtable relative to the door of a room? 9Pq - 9! 362,880 *There are 362, 880 ways 9 people can be seated on a roundtable. 7. What is the number of possible arrangements There are 12 ways"the girls and boys can of ten books on a shelf where four Algebra bt scated alternately books are of the same kind, three Geometry books are of the same kind, and three Statistics books are of the same kind? I0P10= 10 平313 = 6,227,029 800-600,600 TOT 368 There are 600,600 ways the shirts can be sdd 6. How many ways can three boys and three girls be seated alternately at a circular table? P= (n-1)! -(3-1)! = 2! 3! =\ 12 8. Eleven beads, no two of which are the same, are to be strung in a necklace with a clasp. In how many ways can it be done? P= n! = 11! = 39,916,800 =19a958,400 = 3,628,800 -14,200 864 2 *There, are 4,200 possible armangemants There are la,958,400 Ways the beads can be done. of the boolsS. 9. Find permutations of the digits of the number 843,838. GP6=61-20 =60 2121 * There are 60 distinguishable permutations There are 10 ways it can be arrang ed in a liind the number of distinguishable 10. Ana has two vases of the same kind and three candle stands of the same kind. In how many ways can shę arrange these items in a line? sPs- 51 5.4321-O 2! 2! 77 12T 12
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...
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check it pls
![1. How many different nine-digit numbers can
be written using the following digits:
2,2,2,7,7,8,8,8, and 8?
2. How many seating arrangements are possible
for six people at a roundtable?
P=Cn-1)!= C6-1)!-3! =|120]
- 54321 -1,260
%3D
3!2!4! ZZ1-2-1-43-2-1
* There are 1,260 different a-digit. n um bers that 3. A clothing store has a certain shirt in four
can be written vsing the foll owing digits.
4. In how many different ways can five keys, no
two of which are the same, be arranged on a
key-ring that has no clasp?
P= (n-1)! = (5-1)! = 41 = 24
There are 120 possible seating arrangenents
sizes: small, medium, large, and extra-large. If
it has three small, four medium, four large, and
two extra-large shirts in stock, in how many
ways can these shirts be sold if each is sold
one after the other?
13P13
3!4!.4!2
There are 600,600 ways the shirts can be sdd
12
2.
%3D
%3D
There are 12 difterent ways that S keys can
br arranged
5. How many ways can nine people be seated at
a roundtable relative to the door of a room?
9Pq= 9! =362,880
There are 362, 880 way s 9 people can be
seated on a roundtable.
7. What is the number of possible arrangements There are 12 ways"the girls and boys can
of ten books on a shelf where four Algebra be seated alternat ely
books are of the same kind, three Geometry
books are of the same kind, and three
Statistics books are of the same kind?
10P10= 10
4:3!3!
There, are 4,200 possible armangemonts
- 6,227,029 800
TO, 368
600,600
%3D
6. How many ways can three boys and three girls
be seated alternately at a circular table?
P= (n-1)! = (3-1)! = 2! 3! = 12
hat
8. Eleven beads, no two of which are the same,
are to be strung in a necklace with a clasp. In
how many ways can it be done?
P= n! = 11!=39,916,800
=19,958,400
= 3,628,800 -4, 200
864
%3D
%3D
%3D
2.
*
*There are la, 958,400 ways the beads
can be done.
of the bool<S.
9. Find
permutations of the digits of the number
843,838.
GPG= G!
the
number
of distinguishable 10. Ana has two vases of the same kind and three
candle stands of the same kind. In how many
ways can she arrange these items in a line?
10
720=60
12
こ
ニ
上モ、1花先iて2
There are 60 distinguishoable permutations k There are lo ways it can be arrang ed in a lind
312!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbf0b839-5ffb-4795-b2a3-da462ef2a273%2Fa780da90-dd67-4631-8084-961adfc73e47%2Fpmmh4x8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. How many different nine-digit numbers can
be written using the following digits:
2,2,2,7,7,8,8,8, and 8?
2. How many seating arrangements are possible
for six people at a roundtable?
P=Cn-1)!= C6-1)!-3! =|120]
- 54321 -1,260
%3D
3!2!4! ZZ1-2-1-43-2-1
* There are 1,260 different a-digit. n um bers that 3. A clothing store has a certain shirt in four
can be written vsing the foll owing digits.
4. In how many different ways can five keys, no
two of which are the same, be arranged on a
key-ring that has no clasp?
P= (n-1)! = (5-1)! = 41 = 24
There are 120 possible seating arrangenents
sizes: small, medium, large, and extra-large. If
it has three small, four medium, four large, and
two extra-large shirts in stock, in how many
ways can these shirts be sold if each is sold
one after the other?
13P13
3!4!.4!2
There are 600,600 ways the shirts can be sdd
12
2.
%3D
%3D
There are 12 difterent ways that S keys can
br arranged
5. How many ways can nine people be seated at
a roundtable relative to the door of a room?
9Pq= 9! =362,880
There are 362, 880 way s 9 people can be
seated on a roundtable.
7. What is the number of possible arrangements There are 12 ways"the girls and boys can
of ten books on a shelf where four Algebra be seated alternat ely
books are of the same kind, three Geometry
books are of the same kind, and three
Statistics books are of the same kind?
10P10= 10
4:3!3!
There, are 4,200 possible armangemonts
- 6,227,029 800
TO, 368
600,600
%3D
6. How many ways can three boys and three girls
be seated alternately at a circular table?
P= (n-1)! = (3-1)! = 2! 3! = 12
hat
8. Eleven beads, no two of which are the same,
are to be strung in a necklace with a clasp. In
how many ways can it be done?
P= n! = 11!=39,916,800
=19,958,400
= 3,628,800 -4, 200
864
%3D
%3D
%3D
2.
*
*There are la, 958,400 ways the beads
can be done.
of the bool<S.
9. Find
permutations of the digits of the number
843,838.
GPG= G!
the
number
of distinguishable 10. Ana has two vases of the same kind and three
candle stands of the same kind. In how many
ways can she arrange these items in a line?
10
720=60
12
こ
ニ
上モ、1花先iて2
There are 60 distinguishoable permutations k There are lo ways it can be arrang ed in a lind
312!
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