Find the number of arrangements of the letters in the word EMERGE in which (a) all the 3 letters E are consecutive; (b) the first letter is E and the last letter is M.

Q: Erin just bought a bag of gumballs with eight different colors of gumballs. One of the colors is…

A: Let X denotes the number of gumballs that Erin will need to pull out of the bag until she gets her…

Q: Tom has 16 blue pencils, of which 12 are striped dark blue and light blue, and the rest are solid…

A: There are 16 blue pencils and 9 red pencils out of which 12 are striped dark blue and light blue and…

Q: A presidential candidate will be visiting 4 cities in Georgia, 2 cities in Mississippi, and 4 cities…

A: This is a counting problem, and we will solve this using the concept of permutations.

Q: Busi's dog gives birth a litter of six puppies, of which 3 are female and 3 are male. Busi wants to…

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Q: Suppose you want to get a license plate. The license plate has to have 3 letters without repetition,…

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Q: Sunwoo’s closet has 18 different styles of jacket. In how many ways can Eric pick out 7 different…

A: Total number of Jackets = 18  Eric need to pick 7 different styles, this can be done in 18C7

Q: teacher prepares 12 assignments for her 3 students. How many different ways can the assignments be…

A: GIVEN DATA,A TEACHER PREPARES 12 ASSIMENTS FOR 3  STUDENTS WE HAVE TO FIND OUT THE NO OF WAYS CAN…

Q: There are 4 men and 5 women in a room. The leader wants a participation from a group of 2 men and 2…

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Q: Jennifer has 4 black bags. She has 15 seeds in the black bags. She has arranged the seeds in the 4…

A: Given : Number of bags = 4 Number of seeds = 15 None of bag is empty and all bags have different…

Q: Mr. and Mrs. Roger want to name their first baby so that its monogram, first, middle, and last name…

A: Combination: A combination is a way of selecting items from the given collection when the order of…

Q: Five letters, A,B,C,D, and E are arranged in a line. How many arrangements are possible if A can’t…

A: Given that:*The letters available to arrange in a line is,A,B,C,D and E.*The letter A can't be…

Q: a. The large books must always be together. b. The first book and last book must always be medium…

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Q: Amy, Brenda, Charles and Darren are playing treasure hunt in the garden numbered from 1 to 100…

A: Given: The total number of boxes is 100, which is numbered from 1 to 100 placed at different…

Q: There are 49 runners in a race, and no ties. In how many ways can the first three finishers be…

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Q: The first box contains 5 apples, the second box contains 7 apples, the third box contains 9 apples…

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Q: Find A - B if A = {4,5,6} , B = {6,7,8}

A: Given ,  A = {4,5,6} B = {6,7,8} We have to find A - B   A - B is the set of all elements of A that…

Q: Alex wants to choose 12 cookies to eat from a package. There are 7 different varieties of cookies to…

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

Q: Determine the number of arrangements of all the letters in the word SUCCESS.

A: We have to determine the number of arrangements of all the letters in the word SUCCESS. Here, total…

Q: Natasha is in a class of 30 students that selects 4 leaders. How many ways are there to select the 4…

A: Given that  Natasha is in a class of 30 students that selects 4 leaders.  To find Number of ways are…

Q: you have 5 pair of white socks and 10 pair of black sock in a drawer. you randomly choose two pair.…

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Q: You are burning a CD for your assignments. You have assignments of 15 different topics. However, you…

A: Note: Hi there! Thank you for posting the question. As there are multiple questions, according to…

Q: s can this be done, if the order of the choices is taken into s can this be done, if the order of…

A: Given Suppose we want to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.

Q: You have 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has a side…

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Q: Convener and a Secretary are to be chosen from group of people consisting of 50 people. Explain how…

A: i) We can select A as Convener in only 1 way. We can select Secretary from (50-1)=49 people in 49…

Q: A manager has 4 people that can play any of positions. How many

A: In the given situation, there are 4 people that can play any of positions. That is, there are 4…

Q: You are preparing the program for a concert. If the band has 10 songs prepared and will play 6 of…

A: band had 10 songs and play 6 of them .  order of song is important.  no. of ways to do programs = ?

Q: A group of 16 people is choosing a chairperson and Vice- chairperson. They put all 16 people's names…

A: The permutation formula is

Q: Twelve people are to have their picture taken as a group. How many arrangements can there be if Mary…

A: Twelve people are to have their picture taken as a group.Mary has to be first in line and Tim last…

Q: This morning you collected 42 eggs from the hens in your chicken coop. Your 6 favorite neighbors are…

A: Given information: This morning you collected 42 eggs from the hens in your chicken coop. Your 6…

Q: In a class of 60 students , 40 students like math, 36 like math science, 24 like both the subject…

A: Sol:- Given data :-40 students like maths36 students like science24 like both the subjectsi) The…