A set S has 6 elements. How many subsets of S are there with at most 2 elements? (A) 21 (B) 15 (С) 41 (D) 42 (E) 6 (F) 2 (G) 7 (H) 22 E O F B.

Q: Assume that the set S has 7 elements. How many subsets of S have at most 3 elements?

A: Given information- We have given that the set S has 7 elements. We have to find the number of subset…

Q: Q/22 A college planning committee consist of 3 freshmen, 4 sophomores, 5 juniors, and 2 seniors.…

A:

Q: 12. Let B be a subset of A. Let |A| = n and |B| = k. What is the number of subsets of A whose…

A: Given B⊂A. A=n and B=k Now if any subset C of A has 3 elements in intersection with B then C≥3 For…

Q: There are 12 students in a math league competition. a) Cash prizes are given out to the top 3…

A: Given there are 12 students. First prize - 200 $ Second prize - 100 $ Third prize - 50 $ a) 1…

Q: A combination is a selectio objects from а. n objects

A: Combination is a technique which represents the number of possible outcomes from n objects

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: 68. In a city three daily newspapers X, Y, Z are published, 40% of the people of the city read X,…

A: Let the number of people in the city be 100x (where x=0, a constant). Furher assume that A,B and C…

Q: omputer programming team has 9 members. )How many ways can a group of five be chosen to work on a…

A:

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: Your math class has 33 students in the class. a. On Monday the students must choose one of 4…

A: The pigeonhole principal can be used to calculate the total number of pigeon to have at least one in…

Q: Three cards are chosen without replacement from a deck of 52 cards and placed in order from first to…

A: In the deck of 52 cards, there are total 4 6's. (One for each of hearts, diamonds, spades and clubs)…

Q: a restaurant offers 2 different flavours of coffee 3 different soup selection. in how many ways can…

A: Two step multiplication principle: Assume that a taskcan be broken up into two consecutive steps.…

Q: 4. A bakery sells 12 varieties of cupcakes. Assume that it has an unlimited supply of each variety.…

A: Solution..

Q: green A store sells rubber balls in 4 different colors: red, yellow, blue, and If the store has a…

A:

Q: se pigeonhole principle 1. A drawer holds a dozen unmatched brown socks and a dozen unmatched…

A:

Q: How many different ways can you arrange 2 letters from a set of 3 letters {T, S, U} such that…

A:

Q: Assume that A={A,B,C} and B={5,4,1,9,6} A code consists of 2 different symbols selected from X…

A: Given: Assuming X={A,B,C} and Y={5,4,1,9,6}. A code consists of 2 different symbols selected from X…

Q: A bakery sells 10 types of pies: apple, cherry, blueberry, strawberry, peach, key lime, pumpkin,…

A: c) If at least 2 apple and 1 cherry pie are chosen already then 3 spots are already pre selected ,…

Q: A combination of 3 balls are picked at random from a box containing 5 green, 4 white, and 3 black…

A: Hope this is useful.Thankyou

Q: 12 players for a softball team show up for a game: (a) How many ways are there to choose 10 players…

A: a) We can pick a group of 10 players from 12 players in 12C10=66 ways.

Q: List all the permutations of five objects x, y, z, s, and t taken two at a time without repetition.…

A: a) There are total 5 objects. Out of which 2 are to be chosen without repetition, then option B is…

Q: Let A = {1, 2, 3, 4, 5}. How many subsets of A have no more than 3 elements?

A:

Q: How many subsets are there of the set N = {5, 42}?

A: We ahave to find no. Of subsets.

Q: How many ways are there to pick 9 balls from large piles of (identical) red, white and blue balls,…

A: To determine the number of ways to pick 9 balls from large piles of red, white, and blue balls, plus…

Q: Crisha has 5 different colored beads including purple and pink. In how many ways can she arrange the…

A: a). It is given that there are 5 different colored beads. Since there is no restriction on the…

Q: How many of the 60 students in a 25-item quiz can have the same score? 2. Apples, bananas, and…

A: The pigeonhole principle can be used to calculate the least number of objects. The pigeonhole…

Q: Assume that the set S has 7 elements. How many subsets of S have at most 3 elements?

A: Consider that  the set S has 7 elements. The subsets can have 3 elements, 2 elements, 1 element, and…

Q: How many strings of Seven English letters are there A) That contains no vowels, if letters can be…

A:

Q: 5. Four married couples have bought 8 seats in the same row for a concert. In how many. different…

A: a). The number of possible permutations of n object is n!. So, the number of permutation for 8…

Q: At a school education fair, 50 students were interviewed about their interested programmes of study…

A: r  = nA∩B       = student interested in A & Bs = nA∩C       = student interested in A…

Q: How many different ways can you arrange 2 letters from a set of 3 letters {L, S, U} such that…

A: There are 3 distinct letters. We must find the number of ways 2 of these letters can be arranged…

Q: 9. An inventory consists of a list of 115 items, each marked "available" or “unavailable." There are…

A:

Q: A host invites n couples to a party. She wants to ask a subset of the 2n guests to give a speech,…

A: Lets there be n number of couple. We will choose any number of couple and as there are two members…

Q: Using the pigeonhole principle How many numbers must be selected from the set {1, 3, 5, 7, 9, 11,…

A:

Q: How many subsets are there of the set N = {6, 49}?

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: How many ways are there to form a subset of (n| of size k with the property that each selected…

A: Let us define some events   A:- box 1 is selected B:- box 2 is selected E:- Yellow ball is selected

Q: A committee of three is to be selected from a group of six people. How many different committees are…

A:

Q: they are interested in 5 CDs featuring the piano, 4 CDs featuring the trumpet, and 3 CDs featuring…

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: computer programming team has 9 members. a) How many ways can a group of five be chosen to work on a…

A:

Q: A set has 9 elements. How many subsets of S are there with at most 2 elements?

A: Given,            A set has 9 elements. Subsets of S are there with at most 2 elements.

Q: estion 24 According to the Pigeonhole Principle, among any group of 8 people, there must be at least…

A: according to pigeonhole principle

Q: How many subsets are there of the set N = {1, 44, 65, 11, 39, 53, 26}?

A: Given,          The set is N=1, 44, 65, 11, 39, 53, 26We know that,          The number of subsets…

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

A: Determine the number of orders that can be put 7 of the 15 assignments onto the CD. The number of…

Q: A bagel shop has a selection of 8 different kinds of bagels (at least 10 of cach). ( .1) How many…

A: Given, A bagel shop has a selection of 8 different kinds of bagels. At least 10 of each.

Q: A volleyball team consists of 14 players: There are 6 rookies and the rest of the players are…

A:

Q: We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have…

A: Here we will use permutation /arrangement and combination / selection  Number of way r object can be…

Q: 5. Sixteen people on a softball team show up for a game. a) How many ways are there to choose 9…

A: Find the number of ways to choose 9 players out of 16 people.

Q: (a) In a game of UNO, there are cards of 4 colors- red, green, blue and yellow. There are 25 cards…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at 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”.