How many different words consisting of 13 letters can be written such that exactly 4 of the letters are A's, 4 of the letters are B's, 5 of the letters are C's and there are no consecutive A's? Write your answer: the number of ways this can be done is...

How many different words consisting of 13 letters can be written such that exactly 4 of the letters are A's, 4 of the letters are B's, 5 of the letters are C's and there are no consecutive A's? Write your answer: the number of ways this can be done is...

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...

See similar textbooks

Related questions

Q: Suppose we want to choose 5 letters, without replacement, from 15 distinct letters. (a) How many…

A: Solution-: Here, n=15,r=5 We want to choose 5 letter, without replacement from 15 distinct letter.…

Q: For this problem, assume that you are to pick 4 cars from the motor pool, which contains 7…

A: It is given that: n1=n(Subcompact)=7 n2=n(Compact)=4 n3=n(Midsize)=6 Thus, the total number of cars…

Q: In how many ways can a student answer 5 out of 8 questions if he is required to answer 3 of the…

A: Here use combination

Q: A team of 7 players is to be selected from a group of 13 people. In how many ways can this be done?

A: Given data A team of 7 players is to be selected from group of 13 people No of ways can be this…

Q: How many ways can 6 boys stand in a line if a certain boy must come first?

Q: How many ways can 2 students be selected from a group of 5 students if order matters?

A: Solution-: We find number of ways 2 students be selected from a group of 5 students if order…

Q: For this problem, assume there are 9 adjacent seats in a row. How many different ways can 9 people…

A: 9! = 9*8*7*6*5*4*3*2*1 = 362880

Q: I used to babysit Nikki, who had a lot of Beanie Babies. Every time I came she would tell me which…

A: Introduction: According to the combination rule, if r distinct items are to be chosen from n items…

Q: How many 6-places license plates are possible if he first 3 places re to be occupied by letters and…

A: Given data: How many 6-places license plates are possible if he first 3 places are to be occupied by…

Q: In how many ways can a father distribute 7 gifts to his 3 children, if the oldest child receives 3…

A: It is given that one child receives 3 gifts and the other two children receives 2 gifts each.

Q: There are four oranges, five pineapples, and t juice using only two fruits of different types. make…

A: Given: Number of oranges = 4 Number of pineapples = 5 Number of mangoes = 3 Total number of fruits =…

Q: How many ways can three people be selected from a group of seven people if order DOES matter

A: Given that, Total number of peoples = 7

Q: c. There are four oranges, five pineapples, and three mangoes. Suppose you are to make a juice using…

A: c. Given that there are 4 oranges, 5 pineapples and 3 mangoes. Suppose you are to make a juice using…

Q: Three adults and five children are seated randomly in a row. In how many ways can this be done if…

A: Option(1) is correct

Q: 1. When ordering a pizza from Alberto's, you were asked first to choose a type of crust: thin or dep…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: how many ways can Dr. Yes invite 8 of his friends if he has to invite at most 4 at a time?

Q: I. Using the numbers 0, 2, 3, 4, 6, and 8, how many 4-digit odd numbers between 2000 and 8000 can be…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: Six men and eight women are to line up for a picture with the six men in the middle. How many ways…

A: Given that Six men and eight women are to line up for a picture with the six men in the middle How…

Q: How many different ways can 5 out of 8 different shirts, 4 out of 10 different pairs of pants, and 3…

A: We have given that, Shirts = 8 , pairs of pants = 10 and pairs of socks = 6

Q: In how many ways can 5 men and 5 women be seated at a round table if each woman is to be between…

A: We have round table and 5 men and 5 women be seated at round table if each women is to be between…

Q: You have 6 books that you want to donate, and there are 20 poor students. In how many ways you can…

A: The number of ways to select r things out of n is given by the formula nCr=n!r!(n-r)!. First,…

Q: Suppose that I have 250 pieces of candy, I randomly pick 15 of them from the bar and so over that 6…

Q: In how many ways can four boys and five girls sit in a row if the boys and girls must sit…

Q: Four numbers are selected from the following list of numbers: -5, -4, -3, - 2, -1, 1, 2, 3, 4; in…

A: Given: Numbers available : -5, -4, -3, - 2, -1, 1, 2, 3, 4 Aim: To select 4 numbers out of the…

Q: In a class , there are 6 boys and 5 girls . How many ways can we form a committee / group / team of…

A: Using permutations and combinations we can solve for the total number of ways in which a group of 6…

Q: You have 7 adult emus and 6 juvenile emus. How many ways are there to choose a group of emus so…

A: no.of adult emus=7no.of juveniles emus=6

Q: In how many ways can 7 women and 7 men partner up for ballroom dancing, if each person has to dance…

A: The number of ways to select r objects from n objects is computed by using the formula of…

Q: If Joe only has room for 2 of his 6 flags on his flagpole, how many different ways can they be…

Q: A woman wants to select 5 pair of shoes from six pairs of red shoes, 4 pairs of white shoes and 3…

A: Pair of shoes women want is 5. Pair of red shoes is 6. Pair of white shoes is 4. Pair of black shoes…

Q: how many ways can a teacher sit 12 students in two rows of 6 chairs if Bobby must sit in the front…

A: Given: Total number of students = 12 Number of seats in each row = 6 Bobby is in first row and Billy…

Q: In a city, the bus route numbers consist of a natural number less than 100, followed one of the…

A: In a city, the bus route numbers consist of a natural number less than 100, followed one of the…

Q: . How many different ways are there of handing out the prizes if (a) the prizes are all the same?…

A: A kindergarten class has 18 children. FIve of the children are selected to receive prizes. Here use…

Q: For this problem, assume that you are to pick 4 cars from the motor pool, which contains 8…

A: Given data: The number of cars to pick is r=4. The number of subcompact cars is s=8. The number of…

Q: In how many ways can 6 boys and 7 girls sit in a row if the girls and boys must alternate?

Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fundamental Counting Principle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Test Yourself eS so 1. Find the number of ways of 6 objects; say a, b, c, d, e, f, taken three at a time. In other words, find the number of "three letter words" with distinct letters that can be formed from the above six letters.
Suppose that a college of engineering has seven departments, which we denote by a, b, c, d, e,f, and g. Three of the seven representatives are to be selected to attend a statewide convention. How many ways are there to select the three officers? To solve this I have uploaded a picture of how the notes are shown. My question is how they get the 7!/3!4!? where does 3! and 4! come from? Thanks.
Jessica is grocery shopping and has 16 cherry tomatoes and 12 grape tomatoes in her shopping basket. When she gets home, she prepares her ingredients for lunch, but she forgets which of the tomatoes are cherry and which are grape. She cannot distinguish between the two types of tomatoes, so she just picks 13 tomatoes. How many different sets of 13 tomatoes are possible if there are exactly 7 cherry tomatoes?
Suppose that you must choose three people to meet with a customer. You have nine people to choose from. In how many different ways can you choose these three people?
How many words are formed from all letters of the word MISSISSIPPI that not contain 4 consecutive Ss and not contain 2 consecutive Ps?
A student is to answer 10 out of 13 questions on an exam. (i) How many if he must answer exactly 3 of the first 6 questions? (ii) How many if he must answer at least 3 of the first 5 questions?
There are 3 ways to get from Town A to Town B, 4 ways to get from Town B to Town C, and another 5 ways to get from Town C to Town D. In how many different ways could we get from Town A to Town D?
. Suppose you are working on a ten-digit keypad to open a door. You know the combination is exactly three digits long.1. How many choices are there if you may use a number multiple times and the order matters?2. How many choices are there if you may not use a number multiple times and the order matters?3. How many choices are there if you may not use a number multiple times and the order doesnot matter?4. How many choices are there if you may use a number multiple times and the order does notmatter?
Alex wishes to pack 8 of his 15 shirts on a trip.( All the shirts are different). He does not wish to pack all 3 of his white shirts nor to pack all 3 of his red shirt. ( This means he has 9 shirts that are neither white nor red) how many ways does he have to pack 8 shirts given these two restrictions?