A bag contains four red marbles, three green ones, one lavender one, three yellows, and two orange marbles. How many sets of five marbles include at least three red ones?

Q: A committee has 20 people.  In how many ways can a President, Vice-President, and Secretary be…

A: Note:  Permutation: We kno that, nPr represents the selection an ordered set of ‘r’ objects from a…

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

A: At most one of the yellow ones means 0 or 1 yellow ones. There are 3 yellow marbles.  And…

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

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Q: A restaurant offers 20 appetizers and 40 main courses. In how many ways can a person order a…

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

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

A:

Q: How many different teams of 44 can be chosen from a group of 1818 children and 1515 adults if each…

A: It is given that the number of children is 18 and the number of adults is 15.

Q: How many different teams of 4 can be chosen from a group of 15 children and 17 adults if each team…

A: According to provided data, there is total of 15 children (C) and 17 adults (A). Therefore, the…

Q: A woman has ten skirts and five blouses. Assuming that they all match, how many different…

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Q: A bag contains 2 red marbles, 5 green ones, 1 lavender one, 5 yellows, and 3 orange marbles.  How…

A: Since we are making set, so the order will not matter.   If we select the lavender one, then we can…

Q: A car can comfortably hold a family of five. If two people among the five can drive, how many…

A: To find: The number of different seating arrangements. Given: The total number of family member in a…

Q: If a person can select five books from a list of ten, how many different combinations are there?

A: Given data: The total numbers of books are n=10. The number of books selected is r=5. The expression…

Q: How many ways can a delegation of 4 Republicans, 4 Democrats, and 2 Independents be selected from a…

A:

Q: A basketball team consist of two centers, five forwards and four guards. In how many ways can the…

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Q: A store sells 8 kinds of balloons with at least 30 of each kind. How many different combinations of…

A: 8 kinds of balloons with at least 30 of each kind We have to find how many different combinations of…

Q: In the United States Senate, each state is represented by one junior senator and one senior senator.…

A: From the given information. The total number of states in the Midwest is 12. Each state is…

Q: A club with five members is to choose three​ officers: ​ president, vice-president, and​…

A:

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

A: Given that there are 4 red marbles, 3 green ones, 1 transparent one, 3 yellow ones, and 2 orange…

Q: A student club consists of 10 freshmen and 8 sophomores. How many different four-person committees…

A: A student club consists of 10 freshmen and 8 sophomores.

Q: A softball league has eleven teams. If every team must play every other team once in the first round…

A:

Q: how many ways can those offices be​ filled?

A: Given that: A club has 7 members.

Q: A zoo has six male bears and seven female Two male bears and three female bears will be selected for…

A: Number of male bears=6; Number of female bears = 7 Total number of bears = 6+7=13 The number of…

Q: A jar contains four white balls, eight black balls, and six red balls. In how many ways can two…

A: Given :Total number of balls in a Total number of white balls = 4 Total number of black balls = 8…

Q: A bag contains 4 red marbles, 3 green ones, 1 lavender one, 3 yellows, and 2 orange marbles. How…

A: Since it is set so order does not matter. we will use combination method At least three means 3 or 4…

Q: How many ways can a delegation of 55 Republicans, 55 Democrats, and 22 Independents be selected from…

A: Given data Number of Republicans = 77 Number of Democrats = 77 Number of Independent = 33

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

A: A bag contains  2 Red marbles 2 Green marbles 1 Lavender marble 3 Yellow marbles 4 orange marbles

Q: A club consists of 10 men and 13 women. In how many ways can they choose a president, vice…

A: Question is solved.

Q: In the United States Senate, each state is represented by one junior senator and one senior senator.…

A: It was stated that United States Senate, each state is represented by one junior senator and one…

Q: A restaurant offers 4 appetizers and 6 main courses. In how many ways can a person order a​…

A: One object from m objects can be selected in mP1 ways.

Q: How many bridge hands are possible containing 4 spades, 6 diamonds, 1 club, and 2 hearts

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Q: If a club consists of 18 members, how many different arrangements of president, vice- president, and…

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Q: A bag contains 3 red marbles, 2 green ones, 1 lavender one, 2 yellows, and 2 orange marbles.  How…

A:

Q: A baseball team has 14 players. How many 9​-player batting orders are​ possible?

A: Given : A baseball team has 14 players.

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

A: Solution

Q: A softball league has twelve teams. If every team must play every other team once in the first round…

A: Topic: Permutations and combination

Q: A restaurant offers 8 entrees and 9 desserts. In how many ways can a person order a two-course meal?

A: We can find the answer as below.

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

A: Solution: Given information: Red marbles = 3 Green marbles = 3  Lavender  marble = 1 Yellow marble =…

Q: How many baseball teams of 9 members can be formed from 14 players?

A:

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

A: Solution: From the given information, a bag contains three red marbles, three green ones, one…

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

A: It is given that there are three red marbles, two green marbles, one lavender marbles, two yellow…

Q: A basketball team contains 20 players. If 5 people can be on the court at one time, how many…

A: Total number of players is 20. The number of player to be court at one time is 5.

Q: A man has 4 shirts, 4 pairs of trousers, 3 pairs of socks and 2 pairs of shoes. How many different…

A: Given Number of shirts = 4 Number of trousers = 4 Number of pair of socks = 3 Number of pair of…

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: A bag contains 5 red marbles, 2 green ones, 1 lavender one, 2 yellows, and 3 orange marbles.  How…

A: Since we will make sets, so order does not matter. So we will use combination.  Atmost one of the…

Q: If a club consists of 8 members, how many different arrangements of president, vice-president, and…

A: Given that Number of memebers in a club =8 To find number of different arrangements of…

Q: How many committees of 4 can be made from a group of 20 republicans and 15 democrats if at least 1…

A: Since we need at least 1 republican and at least 1 democrat in the committee. So we pick 1 of each…

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

A: Total number of marbles, n = 3 red + 1 green + 1 lavender + 3 yellow + 3 orange = 11 Number of red…

Q: A girl owns 5 pairs of pants, 5 shirts, 4 ties, and 2 jackets. How many different outfits can the…

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Q: A public health inspector wishes to inspect four restaurants by the end of the week. She has a list…

A: Given: Number of high-risk premises restaurants is 26, that is, x1=26. Number of medium-risk…

Q: If you pick 4 cards without replacement from a standard deck of 52 cards, how many different…

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