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: 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 A = {1, 2, 3, 4, 5, 6, 7, 8). (a) How many subsets of 6 elements does the set A have? subsets…

A:

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: How many subsets with an odd number of elements does a set with 12 elements have?

A: Given that a set contains 12 elements. We need to calculate the total number of subset with an odd…

Q: Assume that there are 55 students: 28 who enjoy tennis, and 14 who enjoy neither tennis nor…

A:

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

A: The different groups that can be formed by choosing r  things from a given set of n different thing…

Q: How many three-digit numbers are possible under each condition? (a) The leading digit cannot be zero…

A: We know that 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits in the number system.

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

A:

Q: A collector of toy vehicles has 12 hot rod cars, 10 pickup trucks, 9 classic cars, and 1 big rig…

A:

Q: Consider the number of different ways in which 3 flags can be displayed on a flagpole, one above the…

A: I am going to solve the problem by using some simple geometry to get the required result of the…

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: How many subsets with an odd number of elements does a set with 10 elements have?

A: To find the total number of subsets with an odd number of elements of a set with 10 elements, first…

Q: A baseball team has 13 possible batters. How many batting orders ofnine players can be made, such…

A: Ans-In this question we are given baseball team has 13 possible batters. and we want to find  how…

Q: how many possible combinations are there for computer password that must contain six letters a…

A: Each of the places can take any letters from A to Z , as no repeat condition is given. Therefore,…

Q: A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A: From the given information, The universal set U with 66 elements has been partitioned into three…

Q: 1 How many elements must a set have if the number of proper subsets of the set is of the total…

A:

Q: How many elements does the successor of a set with n elements have?

A: Successor of the set, A is formed by adding an element {A} to the set. So, successor of A will be A…

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

A:

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

A: We have to find number of unordered sets of two items chosen from four items.

Q: In a group of 11 students, there are 6 females and 5 males How many different 4-member committees…

A:

Q: If n(A) = 5, n(B) = 6, and n(C) = 9, what is the greatest and least number of elements in each of…

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”.