Question

Permutations and Counting 1) A pizza restaurant offers 6 kinds of meat toppings and 4 kinds of vegetable toppings. A pizza comes in 3 different sizes and in 3 different crusts. How many varieties of pizza can one select? 2) How many 3 digit numbers which is an odd number can be formed with the digits 1 up to 9, repetition of digits is allowed? 3) In how many ways can 5 people be seated on a sofa if there are only 3 seats available? 4) How many different arrangements can be done from the letters of the word LOVE? 5) Four math books, three ecology books, two music books and three economics books are to be arranged on a shelf. None of their books are identical. a) How many different permutations of these books are there? b) How many different permutations are there if the books on the same subject are to be grouped together? 6) In how many ways can 7 people be seated in a round table if a) they can sit anywhere? b) 3 particular people must sit next to each other? 7) How many different committees consisting of 8 people can be formed from 12 men and 9 women of equal numbers of men and women have to be chosen? 8) From 5 statisticians and 6 economists a committee consisting of 3 statisticians and 2 economists is to be formed. How many different committees can be formed if one particular economist cannot be on the committee? 9) A hat contains 40 marbles, 16 of which are red and 24 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is a) Red? b) Green? 10) If a letter is chosen at random from the English alphabet, find the probability that the letter a) is a vowel. b) precedes the letter j. c) follows the letter g. 11) If a card is drawn at random from a deck of 52 cards, what is the probability that the card is a) red? b) face card? c) red or face? d) red and face?

Name: permutations and counting 1 a pizza restaurant offers 6 kinds of meat toppings and 4 kinds of vegetable toppings a pizza comes in 3 different sizes and in 3 different crusts how many varieties of pizz
Uploaded: 2023-05-13T12:18:33-08:00
Duration: 7 min 7 s
Channel: Donna Densmore
Description: permutations and counting 1 a pizza restaurant offers 6 kinds of meat toppings and 4 kinds of vegetable toppings a pizza comes in 3 different sizes and in 3 different crusts how many varieties of pizz

Permutations and Counting

1) A pizza restaurant offers 6 kinds of meat toppings and 4 kinds of vegetable toppings. A pizza comes in 3 different sizes and in 3 different crusts. How many varieties of pizza can one select?
2) How many 3 digit numbers which is an odd number can be formed with the digits 1 up to 9, repetition of digits is allowed?
3) In how many ways can 5 people be seated on a sofa if there are only 3 seats available?
4) How many different arrangements can be done from the letters of the word LOVE?
5) Four math books, three ecology books, two music books and three economics books are to be
arranged on a shelf. None of their books are identical.
a) How many different permutations of these books are there?
b) How many different permutations are there if the books on the same subject are to be grouped together?
6) In how many ways can 7 people be seated in a round table if a) they can sit anywhere?
b) 3 particular people must sit next to each other?
7) How many different committees consisting of 8 people can be formed from 12 men and 9 women of equal numbers of men and women have to be chosen?
8) From 5 statisticians and 6 economists a committee consisting of 3 statisticians and 2 economists is to be formed. How many different committees can be formed if one particular economist cannot be on the committee?
9) A hat contains 40 marbles, 16 of which are red and 24 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is
a) Red? b) Green?
10) If a letter is chosen at random from the English alphabet, find the probability that the letter a) is a vowel. b) precedes the letter j. c) follows the letter g.
11) If a card is drawn at random from a deck of 52 cards, what is the probability that the card is a) red? b) face card? c) red or face? d) red and face?

Added by Ef F.

Finite Mathematics and Calculus with Applications

Margaret L. Lial, Raymond N. Greenwell,… 9th Edition

Chapter 8

Instant Answer

Solved by Expert Donna Densmore

05/13/2023

Step 1

So, there are 6 meat toppings * 4 vegetable toppings * 3 sizes * 3 crusts = 216 varieties of pizza. 2) To form a 3-digit odd number, the last digit must be an odd number (1, 3, 5, 7, or 9). There are 5 choices for the last digit, 9 choices for the first digit Show more…

Show all steps

Thanks for your feedback!

Permutations and Counting 1) A pizza restaurant offers 6 kinds of meat toppings and 4 kinds of vegetable toppings. A pizza comes in 3 different sizes and in 3 different crusts. How many varieties of pizza can one select? 2) How many 3 digit numbers which is an odd number can be formed with the digits 1 up to 9, repetition of digits is allowed? 3) In how many ways can 5 people be seated on a sofa if there are only 3 seats available? 4) How many different arrangements can be done from the letters of the word LOVE? 5) Four math books, three ecology books, two music books and three economics books are to be arranged on a shelf. None of their books are identical. a) How many different permutations of these books are there? b) How many different permutations are there if the books on the same subject are to be grouped together? 6) In how many ways can 7 people be seated in a round table if a) they can sit anywhere? b) 3 particular people must sit next to each other? 7) How many different committees consisting of 8 people can be formed from 12 men and 9 women of equal numbers of men and women have to be chosen? 8) From 5 statisticians and 6 economists a committee consisting of 3 statisticians and 2 economists is to be formed. How many different committees can be formed if one particular economist cannot be on the committee? 9) A hat contains 40 marbles, 16 of which are red and 24 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is a) Red? b) Green? 10) If a letter is chosen at random from the English alphabet, find the probability that the letter a) is a vowel. b) precedes the letter j. c) follows the letter g. 11) If a card is drawn at random from a deck of 52 cards, what is the probability that the card is a) red? b) face card? c) red or face? d) red and face?

Play audio

Feedback

Donna Densmore and 76 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 Here to look at and i'm just going to set them all up for you and let you do the calculations.

00:05 So we have a pizza restaurant offers six different kinds of meat toppings and four kinds of vegetables.

00:11 It comes in three sizes and three crusts.

00:15 How many varieties of pizza can one select? well we have to have a crust so we have three of those.

00:21 We have to pick a size so there's three of those.

00:24 We don't have to pick any meat so there's actually seven choices for meat.

00:30 We could pick six or none and then there's actually five for the vegetables because we could pick no vegetables.

00:37 So then we have number two, a three -digit number which an odd number can be formed with the digits up to one to nine.

00:44 So if we want an odd number that means we have to have one, three, five, seven or nine.

00:49 There's five ways to do this.

00:51 We can't have a zero in this first digit because then we wouldn't have a three -digit number.

00:56 So we only have nine ways to pick this one.

00:59 That would be ten.

01:00 We multiply that together.

01:01 I can do that one real quick.

01:03 Number three, how many ways can five people be seated on a sofa if only three seats are available? well it would be five, four and three.

01:12 Two people are going to be left standing.

01:14 Again i can do that one really quick.

01:16 That's going to be sixty.

01:18 So we're going to have number four.

01:20 How many different arrangements can be done from the letters of the word love? well we have to pick the first one then we pick the second one, the third one, the fourth one and then we can multiply that together.

01:32 That's easy again, 24.

01:34 Number five, four math books, three ecology books and two music books and three economics books can be arranged on the shelf.

01:43 None of the books are identical.

01:45 How many different permutations of books are there? so we have how many books? four plus three is seven plus two is eleven plus three is fourteen.

01:58 So we're looking at fourteen factorial of being the number of permutations.

02:04 How many ways? okay then i don't know why we had an a part there.

02:13 Oh how many different permutations are there if the books of the same subject are to be grouped together? so we have four different subjects.

02:22 So we're going to have to go one, two, three, four.

02:26 These can be arranged in four, three, two, one.

02:30 Now those are my subjects.

02:32 Okay so then we have to take within those subjects we have to also multiply that.

02:39 That's going to be what, 24 different ways we're going to arrange the subjects.

02:42 Then we have to look at the individual subjects and how they can be arranged.

02:46 So for the math books those would be four factorial.

02:50 For the ecology books that would be three factorial.

02:54 For the music books there would be two factorial.

02:57 In the ecology three factorial.

02:59 Let's look at number six.

03:03 And how many ways can seven people be seated around a table if they can sit anywhere? well it doesn't matter if we're talking a line or around the table.

03:13 It's the same thing.

03:14 It's going to be seven factorial.

03:16 So we're going to look at b.

03:19 And three particular people must sit next to each other.

03:22 So we're going to have these three people sit next to each other.

03:26 And we don't know which three those are.

03:28 So we're going to have to have, now is where the circle makes, we have to think about right here with one of the people.

03:34 That means the other two people can be over here or over here as long as they sit next to each other.

03:41 So once we pick that person, get my pen back, there's three ways we can pick that person.

03:51 So we can go to one or we could go to one...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace