Suppose you need to enter a 4 digit code to enter a room. d How many such codes have exactly 1 digit which appears twice? e Now suppose you need to press 4 different digits simultaneously in order to unlock the door. Does the order matter? How many such codes exist?

Q: Suppose we want to choose 2 objects, without replacement, from the 3 objects pencil, eraser, and…

A: Topic:- permutation and combinations

Q: From a group of 16 women and 17 men, a researcher wants to randomly select 8 women and 8 men for a…

A:

Q: : A and B each have certain number of oranges.A say to B, "If you give me 10 of your oranges.I will…

A:

Q: Scott has a bag of candies. 2/5 of the candies are red. 3/10 of the candies are green. If there are…

A: Given , In a bag Total Red Candies=12 2/5 of candies are red. And 3/10 of candies are green. We have…

Q: survey of 100 students at New England College showed the following: 47 take English. 49 take…

A: From venn diagram, It can be solved easily. N= 100

Q: Answer each of the following. a. If A has five elements and B has seven elements, how many elements…

A: Recall: If A has m elements and B has n elements then A×B has mn elements.

Q: 1. P(6, 2)*P(5, 3)/P(4,3)

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems. These 2 are…

Q: 3. Answer the following: (i) In how many ways can 3 boys and 2 girls sit in a row? (ii) In how many…

A: Here will use the concept of permutations and arrangment Given that  Number of boys = 3 Number of…

Q: A thin tube stretched across a street counts the number of pairs of wheels that pass over it. A…

A:

Q: Suppose you are ordering a calzone from D.P. Dough. You want 4 distinct toppings, chosen from their…

A: a) Total number of toppings = 13  We have to select four distinct toppings out of 13,  Hence, total…

Q: The number of chickens and goats in a field totals 40. The total number of legs among them is 102.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Frank is inviting 6 friends to dinner. He has 10 close male friends and 20 female friends. How many…

A: Given, No of males = 10 No of females = 20 No of invitations = 6

Q: A survey of 100 students at New England College showed the following: 46 take English. 47 take…

A: We can slove this problem with the help of Venn Diagram:

Q: 13b) Suppose the number of permutations without replacement is 720 and the number of combinations…

A:

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

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: If we have 100 (identical) tennis balls and 40 identical bags to place them in, how many ways are…

A: There are 100 balls and 40 bags, if each bag is non empty then first fill each bag with 1 ball. This…

Q: Because of her work schedule, Molly Kay plans to take classes at 8:00, 10:00, and 11:00. Five…

A: Using the fundamental counting principle, it can be written that if there is a sequence of…

Q: Solve the following: 13) A box contains 5 green, 7 yellow, and 10 orange ping pong balls. How many…

A: As per our guidelines we are suppose to answer only three subparts GivenNo.of green balls=5No.of…

Q: There are 25 students in Mrs.​ Pietz's fifth grade class at an international school. All of the…

A: Given ,          Total no of students=25         No of students can speak English=18        No…

Q: 3 cookies. (b) 3 cookies in a particular order. (c) 3 cookies in a particular order with one only…

A: Here AS PER POLICY I HAVE CALCULATED 3 SUBPART

Q: - How many secret codes can be formed consisting of five letters or four digits (but not both), if…

A: If the code has 5 letters.Then we can select each letter in 26 ways. So we can select 5 letters in…

Q: t State U, 45 students are working toward K¨C8 teaching credentials in the new undergraduate…

A: According to the given information ,                        Where; X ( number of students  who…

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: ​​​​​​3 ice cream cones cost $9. At this rate, how much do 2 ice cream cones cost? $

A: Consider the equation

Q: Solve the following problems by applying the basic operations of sets and Venn diagram. 2.- 120…

A: Let us denote C=owns a car D=owns a DVD player S=all families Given that n(C)=70, n(D)=30, n(C ∩…

Q: Assume that n(U)=130, n(B′)=62, n(A∩B′)=31 , and n(A∩B)=35. Find n(A∪B):

A: Given that n(U)=130, n(B′)=62, n(A∩B′)=31 , and n(A∩B)=35.   From n(B′)=62 we…

Q: Shirley and Ben are going souvenir hunting. They come across a store that sells all sorts of…

A: (i) The objective is to find the number of ways to assign 75 key chains in 6 bags. That is, 75 key…

Q: Suppose you are ordering a calzone from D.P. Dough. You want 6 distinct toppings, chosen from their…

A:

Q: Q)1 a) How many 3 digits passcodes are there if first digit must be a 1 or 2 ?   b) How many 3…

A: Q1) a) There are 10 digits 0,1,2,3,4,5,6,7,8,9. The 3 digit passcodes must be formed such that first…

Q: Determine whether the given problem/situation isn a combination or not. Write C if it is a…

A: here use definition of combination  combination is used for counting in which object's order does…

Q: Please answer with explanation. I will really upvote. Thanks

A:

Q: You are hit by what you think is a cow, but realize it is a smart car. You know the first three…

A:

Q: Johnny is a very picky eater, so he likes to use a lot of condiments. He has ketchup, salt, pepper,…

A: In this problem, different cases have been evaluated to solve the question and the number of ways in…

Q: a bag contains 6 red balls and 4 white balls. In how many ways can one draw: a. 2 white balls b. 2…

A:

Q: Mr powers is taking his 2 grandsons to Boston burger , he orders a burger that costs $17 and a…

A: We have to find the cost meal

Q: C. Solve the problem using Venn Diagram. In a group of 36 first year college male students, 22 like…

A:

Q: 4. It is your little brother's birthday, and he has invited 5 of his friends to come to his party.…

A:

Q: Consider the following problem: In Ms. Brown’s class, there are 24 students. There are 6 more girls…

A: Given 24 students in class And 6 more girls than boys

Q: H.W. a) In how many ways can 3 boys and 3 girls sit in a row? b) In how many ways can 3 boys and 3…

A: As per the Bartleby guideline if more than three subparts is asked only first three to be answered…

Q: A box contains 5 red balls, 7 green balls, and 6 yellow balls. In how many ways can 6 balls be…

A: .

Q: Ben has some apples. 9 are red apples. 7 are yellow apples. He gives all the yellow apples to Andy.…

A: Given number of red apples = 9 number of yellow apple = 7 Ben gives all the yellow apple to Andy Now…

Q: 15. There are 3 ways to get from Town A to Town B, 4 ways to get from Town B to Town C, and another…

A: Given Number of ways to get from town A to B = 3 ways Number of ways to get from town B to C = 4…

Q: Suppose we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk,…

A: topic- permutation and combinations

Q: Represent the problem with Venn diagram and answer the question based on the diagram. Twenty-four…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

Q: 1. Ater studying open senior high school. Mary is minking whether or not to pursue a degree in in…

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

Q: 20 politicians are having a tea party, 6 Democrats and 14 Republicans. To prepare, they need to…

A: The number of democrats in a tea party is 6. The number of republican leader in tea party is 14.…

Q: istributing 1000 jobs to 7 servers (we are only interested in how many jobs each server gets). (a)…

A:

Q: he trip consists of a  2 1 4 hour  flight from Atlanta to Dallas, a  1 1 2 hour  layover in Dallas,…

A: Consider the timing individually and convert them into fractions from mixed fractions: Atlanta to…

Q: Suppose you are ordering a calzone from D.P. Dough. You want 8 distinct toppings, chosen from their…

A: Please find the answer in next step.

Q: f 4 men and 5 women are having lunch together (a) in how many different ways can they order 2…

A: In the first part who gets what meal is not specified, there are 9 people, therefore 9 people can…

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.