A bag contains 3 red marbles, 2 green ones, 1 lavender one, 2 yellows, and 2 orange marbles.  How many sets of five marbles include at least two red ones?

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…

A:

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

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Q: How many license plates consisting of three letters followed by three digits contain no letter or…

A: Here we have to find  out the combination of licence plate where repetition  of  letters and digits…

Q: A university hires 7 male instructors and 4 female instructors. In how many ways can it choose from…

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Q: A committee of 6 people is chosen from 7 women and 7 men. How many different committees are possible…

A: Since it is a group of persons so the arrangement does not matter.  We will have to use the…

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 class of 50 students consists of twenty four boys and 26.how many different ways can 5 students be…

A: Given: A class of 50 students with 24 boys and 26 girls are there. Now ,total of 5 students are…

Q: A girl owns 6 pairs of pants, 7 shirts, 6 ties, and 2 jackets. How many different outfits can the…

A: Since it is given that the A girl owns 6 pairs of pants, 7 shirts, 6 ties, and 2 jackets.

Q: A softball league has 13 teams. If every team must play every other team once in the first round of…

A: We are given that there are 13 teams and every team needs to play against every other team. For exam…

Q: In a certain pizzeria you can choose among 3 sizes, 2 crust options, and 5 toppings. If it is…

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Q: A semiconductor company will hire 8 men and 5 women. In how many ways can the company choose from 12…

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Q: If 3 Americans, 4 British people and 2 French people are to be seated in a row, how many seating…

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Q: In a bucket there are 5 purple, 15 gray and 25 green balls. If the ball is picked up randomly, how…

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Q: A pile of soft drink bottle caps has 1 cap on the top layer, 2 caps on the next layer, 3 caps on the…

A: So basically the number of bottle caps in the next layer is just one more than the previous layer.…

Q: There are 4 purple plates and 4 blue plates? How many different ways can the plates be stacked? Two…

A: see the hand written solution:

Q: A company has 12 male and 11 female employees, and needs to nominate 2 men and 2 women for the…

A: Given information is : A company has 12 male and 11 female employees. What to find..... company…

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 drawer contains 20 pens, of which 4 are green, 7 are orange, and 9 are black. At the least, how…

A: Given Data: Number of green pens=4 Number of orange pens=7 Number of black pens=9   Total number of…

Q: The group of qualified candidates for five positions is made up of eight women and six men. How many…

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Q: There are 6 women and 9 men signed up to join a swing dance class. In how many ways can the…

A: Given Information: There are 6 women and 9 men signed up to join a swing dance class. We are asked…

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: The qualified applicant pool for five management trainee positions consists of six women and five…

A: According to the provided information,  6 woman and 5 man  Total number of members = 11 5 management…

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: There are 9 women and 8 men signed up to join a swing dance class. In how many ways can the…

A: Given:  no of women=9  no of men=8  nonof ways to choose 8 people to join 2 or fewer must be men??

Q: How many committees of six can be formed from 17 Republicans and 14 Democrats if three members of…

A: Given : 17 Republicans and 14 Democrats

Q: The Senate in a certain state is comprised of 53​ Republicans, 44 Democrats, and 33 Indeependents.…

A: The number of ways to select 33 Republicans is 53C33.The number of ways to select 22 Democrats is…

Q: The Senate in a certain state is comprised of 54 Republicans, 45 Democrats, and 1 Independent. How…

A:

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: The senate in a certain state is comprised of 59 Republicans, 38 Democrats, and 3 Inpendents. How…

A: Given that the senate in a certain state is comprised of 59 Republicans, 38 Democrats, and 3…

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

A: Given : A baseball team has 14 players.

Q: From 6 female employees and 5 male employees, how many groups of 5 employees can be organized…

A: There are 6 female employees and 5 male employees.

Q: There are 156 players on 13 teams. How many players are on each team? players

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Q: A poker hand consists of five cards from a deck of 52.  Order does not matter.  In how many ways can…

A: A poker hand consists of five cards from a deck of 52.   Order does not matter i.e. combination is…

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 dish contains 2 yellow, 4 red, 5 purple, 2 green, and 3 orange candies.  How many sets of 7…

A:

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

A:

Q: A committee of 4 people is chosen from 8 women and 8 men. How many different committees are possible…

A: Combination: The number of different selections of ‘r’ elements (order doesn’t matter) from a set of…

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 four red marbles, three green ones, one lavender one, three yellows, and two orange…

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

Q: The Senate in a certain state is comprised of 51 Republicans, 48 Democrats, and 1 Independent. How…

A:

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

A: Given dataRepublicans = 4Democrats = 4Independent = 3

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: A drawer contains 20 pens, of which 4 are red, 7 are black, and 9 are blue. At the least, how many…

A: Given Data: Number of red pens=4 Number of black pens=7 Number of blue pens=9   Total number of…

Q: A president, a treasurer, and a secretary are to be chosen from a committee with 44 members. In how…

A:

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…

A: