a set of marbles consisting of 4 red, 3 green, 2 blue, 3 orange, 2 yellow and 3 purple marbles. How many sets of six marbles include at least one blue marble?

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

A:

Q: How many three numbers with no repeated digits, can be formed by the use of the digits 0, 2, 3, 4,…

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: 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 baseball team has 13 members: 10 male and 3 female. How many ways are there for choosing a roster…

A: Given that a baseball team has 13 members: 10 males and 3 females,

Q: A boy has 4 red , 4 yellow and 5 green marbles. In how many ways can the boy arrange the marbles in…

A: Given 4 red, 4 yellow and 5 green marbles

Q: How many ways that two girls and 4 boys can fall in a line of there must be a girl and a boy in the…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: A group of 11 people consisting of 1 freshmen, 3 sophomores, 3 juniors, and 4 seniors are selected…

A:

Q: A committee of six people is chosen from eight women and seven men.  How many          different…

A: Solution: From the given information, there are 8 women and 7 men. Here, 6 people are chosen at…

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

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

Q: A book club offers a choice of 2 books from a list of 20.  In how many ways can a member make a…

A: Since the order of the books matters so we will use the permutation method here.  There are total 20…

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

A:

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: 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 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: 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: How many outfits can be constructed with 1 shirt, 1 pants, and 1 tie from a wardrobe of 2 shirts, 5…

A: The given problem is based on combination {Because order doesn't matter}. The combination of…

Q: A person has 8 friends, of whom 5 will be invited to a party.How many choices are there if 2 of the…

A: Combination Rule:The arrangement of r objects from n different objects is given by:

Q: A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes…

A: Producer Rule: if one event can occur in m ways and a second event can occure in n ways the numbers…

Q: How many ways that 2 girls and 4 boys can fall in a line of there must be a girl and a boy in the…

A:

Q: Each marble bag sold by Deshaun's Marble Company contains 5 orange marbles for every 6 green…

A:

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

A:

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

A: Solution

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: A large pile of coins consists of pennies, nickels, dimes, and quarters (at least 20 of each). How…

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

Q: A team of 5 people will be selected out of 9 boys and 14 girls. How many different teams can be…

A: Given that, Total number of girl = 14 Total number of boy = 9 We have to find number of different…

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: 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 team of five is chosen from six men and four women. How many contain at least one of each sex?

A: Number of women = 4 Number of men = 6  Total number of men and women = 10

Q: A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes…

A: Here , particular brand of shirt comes in 12 colors. It has female version and male version. And it…

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: Suppose eight team members are girls and six are boys, How many groups of seven can be chosen that…

A: Let n denote the total number of girls, then n=8. Let m denote the total number of boys, then m=6.…

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: In a certain country, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6,…

A:

Q: a club consists of 5 men and 4 women. in how many ways can this club elect a president, Vice…

A: Given data A club consists of 5 men and 4 women

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 group of 13 people consisting of 3 freshmen, 2 sophomores, 4 juniors, and 4 seniors are selected…

A: Given: A group of 13 people is to be formed by selecting, 3 freshmen out of 6 freshmen, 2 sophomores…

Q: A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are selected…

A: Given:A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are…

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: In a class, 96% students have at least one smartphone, 98% have a calculator, and 95% have a…

A:

Q: A teacher will randomly award three students with extra credit. How many possible ways can the…

A: Given that  , a teacher will randomly award three students with extra credit .  Teacher can pick…

Q: There are 125 students in a class. At least how many students came from the same state if there are…

A: There are 125 students and 16 states We divide 125 by 16 to find the least number of students from…

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

A: Determine the number of sets of five marbles include at most one of the red ones but no yellow ones.…