If a set has 8 elements, how many of its subsets have the given   numbers of elements?   (1) at least one elements   (2) at least two elements   (3) less than 7 elements

Q: 3) Sarah writes down random positive integers when she gets bored. Prove that if Sarah writes 1001…

A: Given:  Sarah writes 1001 numbers.  Since there are 10 digits, i.e., there are only 103 = 1000…

Q: How many distinct ten-digit passwords are possible if you must use at least one 26 lower case letter…

A: Given: you must use at least one 26 lower case letter from {a, b, . . . , z}, at least one 26 upper…

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: let S = { 1,2,3,4,5,6,7,8,9,10,11,12,13}  HOW MANY SUBSETS ARE THERE TOTAL how many subsets have…

A: This is a counting problem.

Q: If there is a bird in every branch, there will be an excess bird not on the branch but if there will…

A: Here, it is given to us that: There is a bird for every branch, and if each bird sits on one branch…

Q: How many different passwords are there that contain only digits and lower-case letters and satisfy…

A: Given, no. of digtis = 10  (0 to 9) no. of letters = 26  (a to z) Total = 36 (iii) Password must…

Q: A multiset is a collection of objects, just like a set, but can contain an object more than once…

A:

Q: In is required to seat five men and four women in a row so that the women occupy the even places.…

A: Given that  In is required to seat five men and four women in a row so that the women occupy the…

Q: 2. Suppose that 21 girls and 21 boys enter a mathematics competition. Furthermore, suppose that each…

A: Consider a mathematics competition of 21 girls and 21 boys along with the condition that each…

Q: 5 identical copies of a movie will be stored on 20 computers such that each computer has at most 1…

A: Given: 5 identical copies of a movie will be stored on 20 computers

Q: 3. A committee of 7 people is to be chosen from a group consisting of 7 men and 9 women. If the…

A:

Q: Given nine sets {5,15,16,18}, {2,19,21},{1,9,14,16},{1,6,20}, {3,16,21},{5,14,20,21},…

A: given : {5,15,16,18}, {2,19,21},{1,9,14,16},{1,6,20}, {3,16,21},{5,14,20,21},…

Q: Six people attend the theater together and sit in a row with exactly six seats. Suppose the group…

A: Given,no.of men =3no.of women=3total no.of people=6

Q: A set contains eighteen elements. How many subsets containing six elements each can be formed from…

A: Since the order in which elements are arranged doesn't matter so use the combination rule to…

Q: A landscaper has 6 different flowering plants and 4 different non-flowering bushes. She needs to…

A: There are several powerful methods for counting objects and sets of objects without actually having…

Q: 5. How many strings of 3 characters are there, such that every character is a lower case letter, the…

A: If there are a ways of doing something and b ways of doing another thing, then there are a · b ways…

Q: A company has 10 different warehouses for storing their inventory. They will be storing 100…

A: Given:-             A company has 10 different warehouses for storing their inventory. They will be…

Q: How many natural numbers are there with a maximum of 7 digits, the sum of which is 31?

A: As per the question we have to find the total number of natural numbers between 0 to 9999999 whose…

Q: 1. The set of counting numbers greater than -1 and less than 9 2. The set of integers satisfying X -…

A: Roster method is to express the set in terms of flower brackets, for example to write the set of…

Q: A bag contains two red marbles, two green ones, one lavender one, four yellows, and three orange…

A:

Q: In a group of people, 68 people can speak English, 45 people can speak in Arabic and 19 people can…

A: It is given that 68 people can speak English, 45 people can speak Arabic and 19 people can speak…

Q: A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the…

A:

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

A:

Q: A multiset is similar to a set, but can contain an element more than once. How many multisets can we…

A: You can identify every multiset with an ordered pair of usual sets, call them high and low. If you…

Q: A club has seven members. Three are to be chosen as a group to a national meeting. A) If the club…

A: Given Information:  Number of members in a group = 7  Number of men = 4  Number of women = 3

Q: Maximum number of possible subsets of a set having 4 elements is 18. Select one: True False

A: We have to check

Q: Assume there are 3 men and 5 women at a party. Show that if these people are lined up in a row, at…

A:

Q: (9) Number of ways to scoop two unordered pairs from a set of 10 different elements. Assume no…

A: Let there are n distinct elements a1,a2,a3, . . . . . . . an And two set A and B, they should be…

Q: How many strings of 7 English letters are there that start and end with the letter T and contain at…

A: Given, we have to make 7 letters string that  will start and end with T    And the string have at…

Q: A password a string that consists of 4 digits from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, followed…

A:

Q: Example 52. A committee consisting of 5 members is to be formed out of 6 men and 4 women. How many…

A:

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: How many strings of three decimal digits

A: Strings of three decimal digits:

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: A password is a string of length 5, each character of which is from the set (x,y,z) of letters.How…

A: There are 3 letters and the password is a string of length 5 characters. When the password uses all…

Q: License plates in a particular state are to consist of 3 digits followed by 2 uppercase letters. How…

A: no.of digits=10  (0 to 10)no.of uppercase letters=26   (A to Z) 9 ways fill it (0 , 2, 3...10) 9…

Q: Each student has a password, which is 6-8 characters long and each character is either a digit or a…

A: We can solve this using given data

Q: A fruit grower packs apples in boxes. Each box contains at least 220 apples and at most 231 apples.…

A:

Q: A basket holds a set of balls. Each ball is red, green, or blue. How many balls must there be in the…

A: We have given that A basket holds a set of balls. Each ball is red, green, or blue. How many balls…

Q: A set contains (2n + 1) elements. If the number of subsets of this set which contains at most n…

A: Number of subsets which contains atmost n elements is 2n+1C0 + 2n+1C1+....+2n+1Cn = 22n

Q: set of two - digit numbers obtained from the digits 1

A:

Q: Ten men and ten women are to be put in a row. Find the number of possible rows if no two of the same…

A: Given : number of men:10 Number of women: 10

Q: 5 can be formed if the alphabet (set of avail

A: To find: Number of strings of length 5 that can be formed with {a,b,c} with last character not as b.

Q: A woman wants to get to two destinations, A and B. From home to A there are 7 possible routes. From…

A:

Q: A password has n characters ordered in a row. Each character can be either a letter A,B,C or a…

A:

Q: Five men and three women are to be seated in a row of 8 chairs. How many different seating…

A: First find the total number of cases, here there are 8 chairs and 8 persons, so a total number of…

Q: A student can choose a computer project from one of the three lists, or an electronics project list.…

A: Given that: The number of computer projects is 3 which contain 12, 21 and 5 possible projects.…

Q: a class, 100 students play cricket ,120 play hockey and 150 play Tennis. For every 5 students who…

A:

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: Four consecutive positive integers are such that the smallest is a multiple of 5, the second is a…

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.