Consider a bag containing four red marbles, three green ones, one transparent one, three yellow ones, and three orange ones. How many sets of five marbles include at least two yellow ones? sets

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: A student is given a reading list of ten books from which he must select four an outside reading…

A: The total number of books in the reading list is 10. The student has to select 4 books out of 10…

Q: In a standard deck of 52 cards, how many different four-card hands can be formed with at most 2…

A:

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 five-card poker hands containing exactly one pair are possible from a deck of 52 cards?

A: To find n(S), determine the number of ways to choose five-card hands from a pack of 52 cards.…

Q: Given a deck of 52 playing cards, in how many ways can a hand of 5 cards be dealt such that all are…

A: Given: The total number of cards in a deck is 52. The total number of the numbered cards in a deck…

Q: How many six-person volleyball teams be made from a group of ten men and three women if: a.There is…

A:

Q: Consider a bag containing five red marbles, three green ones, one transparent one, three yellow…

A: The five marbles(none of them are red or green) to be selected from a bag containing 5…

Q: Given a deck of 52 playing cards, in how many ways can a hand of 5 cards be dealt such that exactly…

A:

Q: And a standard deck of cards, if the order in which cards are dealt is not important. How many hands…

A: There are total 52 cards in a standard deck of cards. There are total 12 face cards in those 52…

Q: Assuming that no one can hold more than one office, how many selections are possible?

A: select a president, vice-president, secretary, and treasurer out of a club with 15 members.  Here…

Q: A credit card company gives each of its customers a 4-digit PIN where each digit is selected from…

A: Multiplication rule of counting:If a task consists of a sequence of choices in which there are ‘a’…

Q: A child has 25 blocks, of which 8 are yellow, 4 are red, 6 are green, 4 orange, and 3 are blue. If…

A: Given, A child has 25 blocks, of which 8 are yellow, 4 are red, 6 are green, 4 orange, and 3 are…

Q: Consider a bag containing six red marbles, two green ones, one transparent one, four yellow ones,…

A: We have 6 Red marbles2 Green marbles1 transparent marble4 yellow marbles2 orange marblesTotal no of…

Q: A shipment of 9 television sets includes three that are defective. In how many ways can a hotel…

A:

Q: A family has nine children. If this family has exactly five boys​, how many different birth and…

A: Given,A family has 9 childrens

Q: How many ways are there to pair 2n people?

A: We need to compute the number of ways in which 2n people can be paired.

Q: How many different eleven-member football teams can be formed from a possible 35 players if…

A: Total no. of possible players = 35 No. of players in a team=11

Q: Assume that a grade of A,B,C,D, or F is assigned to each of 9 students. In how many ways can grades…

A: From the provided information, The grades are A, B, C, D or F Total students = 9

Q: In a 5-element set, how many partitions can be formed?

A: The number of ways that a set can be partitioned is it's Bell Number  Let S(n, k) be total number of…

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

A: Given that, There are Seven members in a club who need to participate in a national meeting in…

Q: A shipment of 10 television sets includes three thatare defective. In how many ways can a hotel…

A: Consider that the load is of 10 televisions and three of these are defective. Also, consider that…

Q: A student committee is to consist of 2 freshmen, 4 sophomores, 3 juniors, and 5 seniors. If 11…

A:

Q: in how many ways can a hand of 5 cards be dealt such that 2 are black and 3 red cards?

A: Given:  There are 52 cards on the deck. There are 26 red and 26 black cards on the deck. Formula…

Q: An overnight express company must include thirteen cities on its route. How many different routes…

A:

Q: Consider a bag containing four red marbles, two green ones, one transparent one, three yellow ones,…

A: Total number of marbles = 4+2+1+3+3 = 13 Find the sets of five marbles containing 2 yellow marbles:…

Q: From a group of 4 men and 5 women, how many committees of size 3 are possible a) With no…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: Suppose the group of twelve consists of five men and seven women. a) How many five-person teams can…

A: A group consist of fire men and sexes women. We have to make a fire person team with 3men and 2…

Q: There are five people at a volleyball tournament. In how many ways can a team of three be chosen?

A: The number of ways r items can be chosen out of n items is equal to C(n,r) . The formula for C(n,r)…

Q: If radio station call letters must begin with either K or W and must include either two or three…

A: Multiplication Rule of Counting:If there are p selections for the 1st option, q selection for the…

Q: A man has eight shirts and three ties. Assuming that they all match, how many different…

A: Given that, Man has 8 shirts and 3 ties How many different combinations can he wear?

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

A: There are number of marbles in bag: Number of red marbles: 4 Number of green marbles: 3  Number of…

Q: Consider a shipment of 50 laptops of which four are defective. A. In how many ways can we select…

A:

Q: four cards labeled a,b,c and d are randomly placed in four boxes labeled a,b,c, and d. each box…

A: For first card there are 4 choices for next one there will be 3 choices and so on,...

Q: How many five-card hands (drawn from a standard deck) contain exactly two spades? (A five-card hand…

A: There are 13 spades in a deck of 52 cards. We can select 2 spades in 13C2=78 ways.

Q: In a group of 6 boys and 4 girls, 4 children are to be selected. In how many ways can they be…

A: The number of ways in which r different items can be selected from n different items, can be given…

Q: In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are…

A: As per guidelines expert gave to answer first question only

Q: In how many ways can 5 boys and 4 girls be arranged on a bench if there is no restriction? How about…

A:

Q: In a group of 4 people, is it possible for each person to have exactly 3 friends? Why?

A: Let G be a graph with 4 vertices, one vertex representing each person in the group. Join two…

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: If a club consists of 13 ​members, how many different arrangements of​ president, vice-president,…

A:

Q: Given a class of 12 girls and 10 boys. In how many ways can a committee of five consisting of at…

A: Given aclass of 12 girls and 10 biys

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

A: According to the given information in this question We need to find the value of C(8,4)

Q: A man has eight shirts and five ties. Assuming that they all match, how many different shirt-and-tie…

A: Given,            A man has eight shirts and five ties.

Q: Find the number of full houses in a poker hand, that is, the number of poker hands with three of a…

A: Let there be 4C3 =4 by choosing the 3 cards of the same typesand 4C3 =6  by choosing…

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: Consider a bag containing five red marbles, three green ones, one transparent one, three yellow…

A:

Q: Consider a bag containing six red marbles, two green ones, one transparent one, seven yellow ones,…

A: Use combination theorem:

Q: If a club consists of 15 ​members, how many different arrangements of​ president, vice-president,…

A:

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.