An urn contains 5 red balls, 4 green balls, and 1 white ball. Three are drawn simultaneously. Answer the following questions: How many ways can 1 ball of each color be drawn? How many ways can at least 1 green ball be drawn? How many ways can the same color ball be drawn?

Q: There are 12 people in a dinner gathering. In how many ways can they arrange themselves around a…

A: We use permutations and combinations. Number of ways to arrange n objects in n places is n! Number…

Q: During a birthday party, how many ways can five guests, both parents, and the birthday celebrant be…

A: Follow the steps.

Q: A jar contains 5 white balls, 8 black balls, and 6 red balls. In how many ways can 5 balls be…

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Q: If 5 cards are dealt from a standard deck of cards, how many different ways can three clubs and two…

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Q: An urn contains seven ​red, five ​white, and six blue marbles. How many ways can three marbles be…

A: Given that the urn contains seven red, five white, and six blue marbles.

Q: Six people are about to enter a cave in a single row. In how many ways could the arrange themselves…

A: Given: Six people are about to enter a cave in a single row

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: An urn contains 3 red balls, 5 green balls, and 2 yellow balls. (a) If you draw 3 balls, in how many…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 2. A clothing store wants to stock sweatshirts that come in four sizes (small, medium, large,…

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Q: A man has 3 different pairs of shoes, 8 different pairs of socks, 4 different pairs of slacks, and 2…

A: We have given that 3 different pairs of shoes 8 different pairs of socks  4 different pairs of…

Q: At a ballroom dance lesson, the instructor chooses 3 men and 3 women to demonstrate a new pattern.…

A: There are 9 women and 7 men in the class, the instructor chooses 3 men and 3 women to demonstrate a…

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 club has 35 members, 8 of whom are Civil Engineers. In how many ways can a committee of 4 be…

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Q: How many arrangements are there if 8 playing cards are drawn from a deck of 52 cards?

A: If 8 cards are to be drawn from 52 cards, then n=52 and r=8.

Q: How many different patchwork quilts, four patches long and three patches wide, can be made from five…

A: Given: Five red and seven blue squares.   To determine: The number of different patchwork quilts…

Q: A pizza shop offers 15 toppings. How many different 3-topping pizzas can be formed?

A: Total number of toppings are 15.

Q: A bride is choosing a dress for her bridesmaids. If there are 3 styles, 5 colors, and 4 fabrics, in…

A: Given: Styles = 3 Colors = 5 Fabrics = 4 The number of ways that she can select the bridesmaids…

Q: A bag contains 15 pieces of candy. In how many ways can four pieces be selected?

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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: An urn contains 6 green balls and 7 red balls. A man selects balls at random without looking at…

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Q: In how many ways can 16 balls be drawn from an urn containing 3 red balls, 8 white balls, and 5 blue…

A: We have given that,  Red balls = 3  White balls= 8  Blue  balls= 5 Then,  We wil find the how many…

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

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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 urn contains 8 red balls, 3 green balls, and 1 white ball. Three are drawn simultaneously. Answer…

A: Given information: Number of red balls, r = 8 Number of green balls, g = 3 Number of white balls, w…

Q: a restauranr offers 4 different flavors of coffee,3 different soup selections and 4 different…

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Q: 2. Dylan, Andrew, Hailey, and Jordan ran in a race of 25 people. In how many different orders can…

A: 2. There are 4 people Dylan,Andrew,Hailey and Jordan Here The places are also 4 The race are start…

Q: The soccer team has 20 members and will elect P, VP, T and S. In how many ways can this be done?

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Q: Five cards are selected out of 52. In how many different ways can this be done if: they contain the…

A: total cards are 52 cards.  they are 13 clubs , 13 spades , 13 hearts ,13 diamonds clubs and spades…

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: A president, a treasurer, and a secretary are to be chosen from a committee with 30 members. In how…

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Q: If a coin is flipped 10 times, how often are there 6 or more heads?

A: We want to find the probability  P(X≥6)= ?

Q: A health inspector must visit 3 of 8 restaurants on Monday. In how many ways can she pick the 3…

A: Total number of restaurants is = 8  She has to pick 3 restaurants.  Here the arrangement does not…

Q: An urn contains 3 red balls, 5 green balls, and 2 yellow balls. (a) If you draw 3 balls, in how many…

A: (a). Identify the number of different ways to pick exactly 1 yellow ball: The number of red balls is…

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

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Q: If there are 13 employees in a club, in how many ways can they choose a dishwasher and a bouncer?

A: Given information- We have given that there are 13 employees in a club. They want to choose a…

Q: Your sister is shopping at an exclusive Rodeo Drive clothing store and examines 4 distinct blouses,…

A: It is given that there are 4 distinct blouses, 5 distinct dresses, and 2 distinct handbags. Since,…

Q: If a club consists of 12 members, how many different arrangements of president, vice-president, and…

A: Given that  a club consists of 12 members. We have to find the number of different arrangements of…

Q: If 20 paintings are entered in an art exhibit, in how many different ways can the judges award a…

A: It is given that, 20 paintings are entered in an art exhibit. Then judge award the first prize to…

Q: How many different choices can be made from 5 red beads, 4 gold beads and 8 blue beads if at least…

A: As per our guidelines we are supposed to answer only one question per post so i am solving first…

Q: Refer to a bag containing 20 balls—six red, six green, and eight purple. In how many ways can we…

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Q: If Kristine were to pull a marble from the jar below randomly, replace and pull another marble 75…

A: There are 15 marbles in the jar labelled 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. 1 Marble is drawn with…

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: In how many ways can you distribute 10 identical balls between Ram, Yuvraj Singh, Mansoor and…

A: Number of way of choosing r objects out of n identical objects =Crn=n!(n-r)!×r!Given:total identical…

Q: From a group of 10 physicians, in how many ways can four people be selected to attend a conference…

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Q: How many ways can 10 people line up if Joey and Sally cannot be next to each other? If the same…

A: here we have to use permutation ( arrangement )  Number of way r object can be arranged by taking…

Q: How many dierent 6 card hands can be dealt from a deck of 52 cards

A: This question related to the topic combination.

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

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Q: If there are 22 members in a club, how many ways can a President, VP, Secretary, and Treasurer be…

A:

Q: If there are 10 people and only 6 chairs are available, in how many ways can they be seated?

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.