Identify if it's a problem with permutations, combinations, or neither (e.g. repetitions)  From 30 possible questions, how many ways can a teacher pick 4 to do in-class review, another 4 to put on the quiz, and another 10 to put on the test.

Q: Two coins are randomly drawn from a coin pouch. If there are 5 dimes, 2 nickels, and a quarter, how…

A: As given there are 5 dimes, 2 nickels, and a quarter in a pouch. 1 nickel = 5 cents 1 dime = 10…

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: Two coins are randomly drawn from a coin pouch. If there are 4 dimes, 2 nickels, and a quarter, how…

A: The pouch contains 4 dimes, 2 nickels and one quarter. Two coins are randomly drawn from a pouch.

Q: Two coins are randomly drawn from a coin pouch. If there are 4 dimes, 3 nickels, and a quarter, how…

A: The probability density function of X is obtained below:From the given information, number of coins…

Q: Suppose we want to choose 3 letters, without replacement, from the 4 letters A, B, C, and D.

A: We want to choose 3 letters and we have 4 letters A,B,C and D, we have to determine (a) How many…

Q: In how many ways can a baseball coach prepare a batting order if: The coach still has to select the…

A: From the provided information, Total players = 12

Q: In how many ways can you choose 5 out of 11 people for a game of basketball?

A: In how many ways can you choose 5 out of 11 people for a game of basketball. Here i attached…

Q: Decide if the situation is a permutation or a combination and then answer the question.   A musician…

A:

Q: Does the problem, 'A medical researcher needs 6 people to test the effectiveness of an experimental…

A: A medical researcher needs 6 people to test the effectiveness of an experimental drug and 13 people…

Q: In how many ways can you choose 3 gifts from a bag containing 4 different gifts?

A: It ia given that Total gifts n  = 4 Selected gifts r = 3

Q: Suppose we want to choose 5 letters, without replacement, from 18 distinct letters. (a) How many…

A: (a)   Determine the number of ways that the 5 letters can be selected from 18 distinct letters…

Q: This problem involves permutations. A pianist plans to play seven pieces at a recital. In how many…

A: (1) There are seven pieces at a recital we can arrange the 7 pieces of recital in 7! ways…

Q: Suppose we want to choose 2 letters, without replacement, from the 4 letters A, B, C, and D. (a) How…

A:

Q: It's all about PERMUTATION - I'm how many different ways can 5 bicycles be parked if there are 7…

A: Given: n=7r=5 The number of ways 5 bicycles be parked in 7 available parking spaces is obtained as…

Q: The number of permutation of n items is also called as _______________.

A: We have to fill the blank with the correct information -  The number of permutation of n items is…

Q: How many ways are there to choose first, second, and third prizes in an art contest with 18 entries?

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

Q: (a) How many ways can a student choose eight out of ten questions to answer on an exam? (b) How many…

A: (a) total number of question=10 to find number of ways can a student choose eight out of ten  we…

Q: Determine whether the following problem involves a permutation or combination.​ (It is not necessary…

A: We have given,Number of people needed to test = 37Total number of people volunteered for this test =…

Q: In how many ways can eight children posing for a photograph line up in a row?

A: 8! = 40320 ways can eight children posing for a photograph line up in a row

Q: b) Suppose that repetition of letters is pemitted, How many 6 letter can be fomed from the letters?

A: Now we have to calculate ,how many 6 letter can be formed if repetition is permitted.

Q: In how many ways can first, second, and third prizes be awarded in a contest with 110 contestants?…

A:

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: 20 fifth graders compete in a spelling bee. If there is a gold medal, silver medal, and bronze medal…

A: We have  Medals = 3 Positions = 3

Q: A bag contains 11 pieces of candy. In how many ways can four pieces be selected? way(s)

A: To find: The number of ways of 4 pieces of be selected.

Q: 2. If you have 7 types of candy, how many pieces of candy would you have to guarantee that you had…

A:

Q: (b) If the order of the choices is not taken into consideration, how many ways can this be done? (a)…

A:

Q: Suppose you are asked to list, in order, the three best movies you have seen this year. If you saw…

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

Q: Ten jokes are listed in a magazine.   If the fourth joke from the magazine is​ excluded, in how…

A: There are 10 jokes listed in a magazine.Here 4th joke is excluded than find the number of ways…

Q: How many ways can a teacher choose 3 out of 8 students for a field trip?

A: Need to find the number of ways a teacher choose 3 out of 8 students for a field trip.Choosing r…

Q: In how many ways can a student choose to do 5 questions out of 11 on a test?

A: The question is based on permutation. We need to find the number of ways a student can choose 5…

Q: Suppose we want to choose 2 letters, without replacement, from the 3 letters A, B, and C. (a) How…

A: (a)   Determine the number of ways that the 2 letters can be selected from three letters without…

Q: In how many possible ways can Juan answer an 8-item matching type quiz if there are also 10 choices…

A:

Q: How many permutations can be made out of the letters in the word CAROLINE taken 4 at a time?

A: There are 8 letters in the word CAROLINE. We can take 4 letters from 8 letters in 8P4=8!(8-4)!=1680…

Q: a. In how many ways can the three-grill displays be selected from the 5 displays?

A: Given that  Number of different displays (n) = 5 But, Only three would be selected . Number of…

Q: A student is to answer 10 out of 15 questions on a midterm test.         a. How many examination…

A: Given that  A student is to answer 10 out of 15 questions on a midterm test. Total number of…

Q: (a) If a student must answer 8 of 12 questions on an examination, how many different selections of…

A: Given:  A student must answer 8 of 12 questions on an examination  To find:a) The different…

Q: Elvis has 12 close friends. How many different combinations of 5 of them may be invited for dinner…

A: w heave to find no. Of combinations possible.

Q: Decide whether you would use a permutation, a combination, or neither. Next, write the solution…

A:

Q: In how many different ways can a student select to answer four questions from a test that has seven…

A:

Q: 1. In your drawer, there are 6 identical pairs of purple socks, 7 identical pairs of polka dot…

A:

Q: b) In how many different ways can five friends sit for a photograph of five chairs in a row?

A: Given :              There are five friends sit for a photograph in a row of five chairs.…

Q: how many ways can a hand of 7 spades be chosen from an ordinary deck?

A: Given that  Ordinary deck of cards Number of ways of can a hand of 7 spades be chosen from ordinary…

Q: The number of permutations of n items is also called as _______________.

A: The number of permutations of n items is also called as n! (n Factorial).

Q: How many ways can you choose 5 out of 10 friends to invite to a dinner party?

A: To solve the problem of combinations (selections) in the given scenario.

Q: In how many ways can the first, second, and third places be chosen from a group of 10 contestants?…

A: Given  Number of contestants = 10

Q: State if the scenario involves a permutation or a combination. Then find the number of…

A: Here we need to select the players and arrange them in the batting order. so we need to do selection…

Q: Decide whether you would use a permutation, a combination, or neither. Next, write the solution…

A: Use permutation

Q: A doctor visits her patients during morning rounds. In how many ways can the doctor visit 8 patients…

A: The number of ways that the doctor can visit 8 patients during the morning rounds is,The number of…

Q: In how many ways can a student select 7 out of 10 questions to work on an exam?

A: Given that, The total number of question to work on an exam is, n=10 The student select number of…

Q: In how many ways can first, second, and third prizes be awarded in a contest with 360 contestants?…

A:

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.