Suppose I had the set {1,2,3} and wanted to make a list of 5 of those elements that contained one element from the set and a pair of duplicates.  For example, (2, 1, 3, 3, 1).  The 2 is the single element and the pair of duplicates is 1,1 and 2,2. How many ways can this be done?

Q: Assume that the committee consists of 10 Republicans and 5 Democrats. A subcommittee consisting of 5…

A: Given Information: Assume that the committee consists of 10 Republicans and 5 Democrats. A…

Q: Consider 2 classes, the first with 5 students, and the second with 7 students. From this group of…

A: Given data 2 classes First with 5 students and second with 7 students 2 students need to be selected

Q: Suppose you had 4 red checker pieces and 5 black checker pieces. How many ways can you arrange these…

A:

Q: A signal can be sent from one location to another by running different colored flags up a flagpole,…

A: Given total number of different colour flags = 15 And first flag is white

Q: Suppose a class consists of 4 students majoring in Mathematics, 3 students majoring in Islamic…

A:

Q: Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert.  In how many ways can…

A: Permutation: A permutation is an arrangement of objects in a definite order. Let n is the total…

Q: A football club has 15Players. Find the possible number of team with 11Players which can be formed…

A: Given Data: Number of players=15   Number of players in a team=11

Q: from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition is not allowed and all the odd digits occur…

A: The biggest possible number is 975,318,642; the digit zero(0) is being excluded from the question…

Q: Suppose that 4 Pistons need to be installed in a new engine block. there is a production run of 100…

A: Given, there is a production run of 100 Pistonsand 4 Pistons need to be installed in a new engine…

Q: How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that the…

A: To form a 3 digit number, we start we can not place 0 on hundreds position since that will make it a…

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one…

A: To find  How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} toguarantee that at least…

Q: Suppose that a coach must select 5 players to play on a basketball team. • The coach has 13 players…

A: The coach has 13 player to select from  And only 4 players can play center, so one of them has to be…

Q: Assume the sales representative calls 5 customers, and each call has 2 possible results: reaches the…

A:

Q: the track team has 20 members and will be sending 5 members to the next competition. how many 5…

A: Combinations: The number of combinations of r items selected from n items is, nr=n!n-r!r! The track…

Q: Suppose any possible arrangement of 8 letters is considered a word and the letters are chosen from…

A:

Q: Suppose that you have a combination lock that uses letters instead of numbers for its combination,…

A: Solution: The total number of letters is 26 and the lock will be opened with four letters and…

Q: • Suppose that a coach must select 5 players to play on a basketball team. • The coach has 12…

A: Given that there are 3 players who can play center. So we can choose center in 3 ways only.  When…

Q: When I arrange the members of a marching band in rows of 2, 3, or 4, there is always 1 person left…

A: To solve the given problem

Q: A license plate has the form YYY-MATH, in which Y is a digit from 1-9, M has to be the number 5, A…

A: First we will find the number of choices for each then multiplying those choices will give us How…

Q: A supermarket wants to send codes for $0.25 off a bag of chips to its rewards program members. Each…

A: There are 24 letters and 7 digits that would be used to generate a coupon with one digit follows by…

Q: A committee has 10 members and 4 members must be chosen for a subcommittee. Three of the 10 members…

A: Statisticians/mathematicians use different counting techniques while selecting or arranging members…

Q: Assume that there are 10 girls and 8 boys in the neighborhood club, and a team of 8 is to be…

A:

Q: bank PIN is a string of four digits, each digit 0-9. How many choices are there for a PIN if the…

A: Given A bank PIN is a string of four digits, each digit 0-9. Odd numbers=1,3,5,7,9

Q: How many elements are in the union of four sets if each of the sets has 95 elements, each pair of…

A: Here, there are four sets. This is representing as A, B, C, and D.Each of the sets has 95…

Q: How many ways are there to list the digits 1, 1, 2, 2, 3, 4, 5 so that the digit 3 and 4 are not in…

A:

Q: Find the number of ways that 6 teachers can be assigned to 4 sections of an introductory psychology…

A: It is given that, 6 teachers can be assigned to 4 sections. We have to find the no. of ways that 6…

Q: A committee of 5 consisting of 3 girls and 2 boys is to be chosen from a class with 15 girls and 10…

A: Given: Total Number of Girls=15Total Number of Boys=10Commitee required 5 candidate in whichNumber…

Q: Suppose a designer has a palette of 16 colors to work with, and wants to design a flag with 2…

A: Recall:  nCr=n!r! (n-r)! We have, n=16, r=2

Q: Show that you can make four distinct lists of books so that the total number of pages in the books…

A: Given: 15 text books is available and each with between 200 and 600 pages

Q: A team of 5 people will be selected out of 9 boys and 14 girls. How many different teams can be…

A: Given that, Total number of girl = 14 Total number of boy = 9 We have to find number of different…

Q: Suppose we want to choose 2 colors, without replacement, from the 5 colors red, blue, green, purple,…

A:

Q: | Suppose 10 ducks and 6 geese line up in a single row. In how many ways can they line up so that no…

A:

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6, 7, 8} to guarantee that at least…

A:

Q: Suppose we went to choose 2 colors, without replacement, from the 4 colors red, blue, green, and…

A:

Q: Find the number of arrangements of the digits {0,1,2,3,4,5,6,7,8,9} such that the first digit is…

A: We need to find the total number of arrangements of digits 0,1,2,3,4,5,6,7,8,9 such that the first…

Q: How many ways are there to permute the elements of the multiset {1,1,2,2,3,4,5,6} so the first and…

A:

Q: A signal can be formed by running different colored flags up a pole, one above the other. Find the…

A:

Q: In a certain country, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6,…

A:

Q: Suppose a designer has a palette of 10 colors to work with, and wants to design a flag with 2…

A:

Q: A committee of 5 students are to be chosen from 25 CS majors and 15 Math majors. How many of these…

A: Exactly 3 CS major students can be selected from 25 CS major students in, 25C3 ways, i.e. 2300 ways.…

Q: Suppose that you must choose three people to meet with a customer. You have nine people to choose…

A: Given data, Total number of people (n)=9 Number of people to meet with a customer (r)=3

Q: itially, 10 people have an infection. The next day, every infected people infects one more person.…

A: To find the number of days it will take for 1280 people to infect.

Q: A total of 50 students are in a class and they are to be divided into groups of 5. How many…

A: Ans - Given,       A total of 50 students are in a class and they are to be divided into groups of…

Q: An oil company is going to issue new ID codes to its employees. Each code will have one letter,…

A:

Q: There are 9 cards each written with the numbers 1, 2, 2, 3, 3, 3, 4, 5 and 6. Cards with odd numbers…

A:

Q: Suppose we want to choose   3 colors, without replacement, from the   4 colors red, blue, green,…

A: Combination: The number of different selections of ‘r’ elements from a set of ‘n’ elements (order…

Q: Suppose 10 baseball players are available to be drafted by 4 teams where each team might win any…

A: Assume the number of players drafted in 4 teams are x , y , z and w. Total number of players = 10…

Q: a committe of 5 people is to be chosen from a group of 6 men and 4 women how many committed are…

A:

Q: Suppose that all the pages are black and white, but each group of 25 consecutivepages (1-25, 26-50,…

A: To determine the number of ways for the 125 pages to assign to the 5 printers. Given that, the total…