For each of the following problems, explain if the problem is one involving permutations or combinations. (It is not necessary to solve the problem.). Solve, a. How many ways can you select 6 free DVDs from a list of 200 DVDs?b. In a race in which there are 50 runners and no ties, in how many ways canthe first three finishers come in?

Q: Suppose thirty-six students signed up for class orientation sessions. If exactly twenty-two of them…

A: Given that, there are 36 students signed up for class orientation session. Number of students signed…

Q: A birthday cake is to have two layers of cake separated by a layer of icing, with another layer of…

A: Let a, b, c, d, e be the different kinds of cake known. Let x, y, z be the 3 different types of…

Q: 2. Suppose you had to travel and you decide to take two of the books from Problem #1. How many…

A: Solution

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: Determine the "n" and "p" in the following problems and write them in Combination notation. a)How…

A: Since, you have posted a question with multiple sub-parts, we have provided answer for first 3…

Q: If I have 3,493 points, right now, and I get 320 points every day, and I want to get 27,650 points,…

A: We have to find number of months to achieve 27650 points.

Q: For each situation below, identify whether it is a permutation or combination problem and then find…

A: Permutation relates to the act of arranging all the members of a set into some sequence or order.…

Q: A birthday cake is to have two layers of cake separated by a layer of icing, with another layer of…

A: Given information: The number of layers is 2. The number of kinds of cake is 5. The number of types…

Q: one family has comfortable children, with four daughters and two sons from a village of 1000 houses,…

A: As per given by the question, one family has comfortable children's with four daughter and two son…

Q: On a Friday morning, the pro shop of a tennis clubhas 14 identical cans of tennis balls. If they are…

A: Let 'n' be the number of days on which tennis balls were sold and 'k' be the number of cans of…

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: 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: If a family has six children, in how many ways could the parents have two boys and four girls?

A:

Q: Janice jogs every 4 days and Jennifer jogs every 3 days. If today is a Tuesday and Janice and…

A: Given, Janice jogs every 4 days and Jennifer jogs every 3 days. Today is a Tuesday and Janice and…

Q: (a) How many ways are there to place 10 paintings into 8 boxes, given there should be at least one…

A: a. The total number of ways of dividing 10 paintings into 8 boxes so at least one painting in each…

Q: When we are considering n objects taken r at a time, with r . 1, why will the number of combinations…

A: "When we are considering n objects taken r at a time, with r . 1, why will the number of…

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: In how many ways may Ana select 5 of her 10 friends to attend her birthday party? In how many ways…

A: Here use combination

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: Answer the following problems: 1) A dance instructor asks each student to do 4 out of the 10 dance…

A: We have given that 10 dance routine. In 10 dance routine, 2 are easy, 5 are moderately difficult and…

Q: Suppose you have 11 books and you randomly pick 4 to take on vacation with you. How many ways can…

A:

Q: A computer user has downloaded 15 songs using an online file-sharing program and wants to create a…

A: Given that the computer use has downloaded 15 songs using an online file-sharing program and wants…

Q: Suppose you are asked to list, in order of preference, the three best movies you have seen this…

A:

Q: If I charged 30$ a hair cut the whole year how many customers would I need to reach 17,510$ and how…

A: From the given information, Charge for a haircut for the whole year = $30 Now, a) to find out how…

Q: a) Construct the appropriate decision tree to help the farmer make the appropriate decisions. This…

A: Solution:

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: Solve the following problems applying Polya’s Four-Step Problem-Solving strategy. Suppose that…

A: Step 1: Understand the problem Total number of students=25 The number of students who signed up for…

Q: From 30 possible questions, how many ways can a teacher pick 4 to do in-class review, another 4 to…

A: Given   n = 30. The required number of ways           =  30 C 4 .26 C 4  .22 C10

Q: Suppose we want to choose 2 letters, without replacement, from the 5 letters A, B, C, D, and E. (a)…

A:

Q: Suppose thirty-two students signed up for classes during an orientation session. If exactly twenty…

A: Follow the next steps for the solution. The detailed step by step solution by Polya's problem…

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

A: Given we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk, and…

Q: A student is to answer 10 out of 13 questions on an exam. (i) How many choices has he? (ii) How many…

A: Note: Hey, since there are multiple subparts posted, we will answer first three subparts. If you…

Q: A birthday cake is to have two layers of cake separated by a layer of icing, with another layer of…

A: Given information: The number of layers is 2. The number of kinds of cake is 3. The number of types…

Q: A computer user has downloaded 22 songs using an online file-sharing program and wants to create a…

A: Here, total number of songs, n= 22 Number of songs to be selected, r = 10

Q: If there are 4 roads from Town A to Town B and 6 roads from Town B to Town C, in how many ways can…

A: Solution:  It is given that there are 4 roads from town A to town B and 6 roads from town B to town…

Q: If you have six books, but there is room for only four books on the shelf, in how many ways can you…

A: From the given information, n=6 and r=4.

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: e number of ways to color ?objects with 3 colors if every color must be used at least once? b....In…

A: To find: Number of different uniforms composed from the items.

Q: If a family has four children, in how many ways could the parents have two boys and two girls?

A:

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

A: topic- permutation and combinations

Q: Suppose thirty-two students signed up for classes during an orientation session. If exactly twenty…

A: Given that: Total number of students = 32Number of students signed up for chemistry =20Number of…

Q: Solve the following problems 1. In how many ways can 9 passengers be seated in a bus if there are…

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

Q: Solve the following: 11)  A committee of 6 officials is to be chosen from 8 men and 7 women. If the…

A:

Q: During a special promotion, a customer purchasing a computer and a printer is given a choice of 3…

A:

Q: In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must…

A: We have to find the possible number of ways to form a committee of 5 members from 5 juniors and 7…

Q: *For the following scenario, state whether it involves a permutation or a combination, then find the…

A:

Q: It’s the first day of summer camp, and the counselors are trying to figure out where one of the…

A: Given: There are four beds available in Cabin #1, five in Cabin #2, and just one in Cabin #3. To…

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

A: Given : 3 objects ( pencil , eraser , desk) to find :  In how many ways 2 object can be choosen…

Q: Suppose you have 11 books and you randomly pick 3 to take on vacation with you. How many ways can…

A: To count the number of possible selections

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.

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.