A credit card company gives each of its customers a 4-digit PIN where each digit is selected from 0,1,2,...,9. How many different PINS are possible?

Q: How many different committees are possible that consist of 5 women and 3 men selected from a group…

A: For a committee, arrangement does not matter so use the combination method.  We can select 5 women…

Q: The eleven players of the CHS sepak takraw team are to be photographed for the team's tarpaulin. In…

A: Here, the question is in how many ways can 11 players can be arranged in a row.

Q: How many outfits can be made from 4 pairs of slacks, 5 shirts, and 3 ties, if one selection from…

A: First decide on a pair of slacks.For that there are 4 different choices.Now for each of those…

Q: Find the number of ways to put eight different books in five boxes, if no box is allowed to be…

A:

Q: A restaurant offers a special pizza with any 5 toppings. If the restaurant has 13 toppings from…

A: Combination: The number of different selections of ‘r’ elements (order doesn’t matter) from a set of…

Q: If a dealer randomly picks 5 cards from a standard deck that consists of 52 playing cards and then…

A: From the above data We are given that Total number of cards = n =52 No of selected cards = r =3

Q: How many 4-digit combinations can be made from the digits 0-9?

A:

Q: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at…

A:

Q: If a phone company sends a random 6-digit number to customers to activate their phone, how many…

A: Consider a problem in which there are n vacant inline spots, each spot is to be filled by any of the…

Q: A club with 29 members is to select a committee of five persons. In how many ways can this be done?

A: In a committee, we select the persons as a group. So the arrangement does not matter. So we will use…

Q: A State's License plates consist of 4 letters followed by 5 digits. How many possible license plates…

A: Given,  License plate consist of 4 letters followed by 5 digits. Since repetition of the letters and…

Q: There are 10 students in a class. In how many ways can an instructor give at most three students a…

A: n = 10 Let x represent the number of students given grade A.   The number of ways a student can be…

Q: An employment agency has 6 temporary workers. In how many ways could 3 of them be assigned to 3…

A: In theory of combinatorics, the way of selecting r objects from n objects with regard to the order…

Q: A race has 10 runners. In how many ways can the first three places be decided?

A: Here use combination

Q: What is the minimum number of students required in a discrete mathematics class to be sure that at…

A: We solve the given problem in next step.

Q: With 20 people seated around a tabke, how many ways can 3 people be selected without any being…

A: It is given that there are 20 people seated around a table. The total number of ways of selecting 3…

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: Out of 9 children, in how many ways can a family have at least 1 girl?

A: We have given that, 9 children i.e. n=9 and family have at least 1 girl i.e. r=1   Combination…

Q: How many unordered sets are possible that contain three objects chosen from seven?

A: Number of unordered sets that contain three objects chosen from seven = 7C3

Q: From a club of 16 people, in how many ways can a group of five members be selected to attend a…

A: Given Data: The number of people in the club is: n=16 The number of members required is: x=5 The…

Q: Suppose that there are 9 female and 12 male students in a classroom. How many different 5-member…

A: According to the provided information, number of female students = 9 number of male students = 12…

Q: There are 10 students in a class. In how many ways can an instructor give at least one student a…

A: There are 10 students So sample size, n= 10 And we've to find ways for at least 1 student. So r= 1

Q: Find the number of different signals that can be made by arranging at least three flags in order on…

A: find the number of different signals that can be made by arranging at least three flags out of 6

Q: How many unordered sets are there of two items chosen from four? sets

A: To Find: How many unordered sets are there of two items chosen from four? Concept: Crn=n!r!n-r!

Q: A shipment of 40 computers are unloaded from the van and tested 6 of them are defective In how many…

A: We will find out the required number of ways.

Q: A softball league has eleven teams. If every te team once in the first round of league play, he…

A:

Q: Suppose that there are 9 female and 12 male students in a classroom. How many different 5-member…

A: Combination:   A combination is a selection of objects where order is not important.   If n is…

Q: What is the minimum number of students required in a Mathematics class test to be sure that at least…

A: We need to use the pigeonhole principle.  We need to find the minimum number of students that are…

Q: Six players are to be selected from an 11​-player baseball team to visit schools to support a summer…

A: No. Of total students = 11 No. Of player to select = 6.

Q: A. How many 3 digit numbers greater than 200 can be made from 0,1,2,3,4,5 if repetition of digits is…

A:

Q: A sailboat owner received 5 different signal flags with his new sailboat. If the order in which the…

A: Given A sailboat owner received 5 different signal flags with his new sailboat.

Q: A cargo ship unloaded a shipment of 12 photocopy machines that contains 3 defective units. In how…

A:

Q: How many different selections of three books can be made from a set of fifteen books?

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

Q: A restaurant offers a special pizza with any 6 toppings. If the restaurant has 11 topping from which…

A:

Q: How many unordered sets are there of five items chosen from eight?

A: In unordered sets, the order of the selection of the selection of items does not matter. So,…

Q: How many 4-person committiees can be formed from a group of 8 teachers and 5 students if there must…

A: If there is 1 teacher, then there must be (4-1)=3 students.  We can pick 1 teacher from 8 teachers…

Q: How many elements are in the set {0, {0}}?

A:

Q: A shipment of 14 television sets includes three that are defective. In how many ways can a hotel…

A: As per our guidelines we suppose to do only one question1.GivenNo.of television =14No.of defective…

Q: How many unordered sets are there of four items chosen from six? sets

A:

Q: A club with 23 members is to select a committee of six persons. In how many ways can this be done?

A: Given: The number of members in a club is equal to 23, To find: The number of ways of selecting a…

Q: Suppose a certain combination lock requires three selections of numbers, each from 1 through 25.…

A: 1 to 25 there are 25 numbers. The numbers may repeat in the combination. For the first number, there…

Q: Eight men and seven women are randomly assigned distinct numbers from 1 to 15. On an average, how…

A: Given: The distinct number given 1 to 15

Q: How many full houses ( one pair and on three of a kind) are possible in 5 card poker?

A: Here we want to all  in 5 houses possible cards.

Q: If a bank sends a random 5-digit number to customers for security, how many potential numbers are…

A:

Q: A bus has 8 vacant seats in the first rows. If 3 additional passengers enter the bus, in how many…

A: For the number of ways of their seating, we need to use combination.

Q: A corporate ID number consists of any three numerical digits, followed by any two letters of the…

A: We have to  find the no. Of ways...

Q: How many six-number combinations can be generated from the numbers from 1 to 42 inclusive, without…

A: Given information: A 6 number combination is to be generated. The possible numbers are selected…

Q: A shipment of 40 computers are unloaded from the van and tested. 6 of them are defective. In how…

A:

Q: How many different ID cards can be made if there are 6 digits on a card and no digur can be used…

A: Given: Number of digits = 6 No digits is used more than once.