At the beginning of a board​ game, players randomly select 3 cones from a group of 10 cones consisting of 6 green cones and 4 blue cones.   Complete parts​ (a) through​ (d) below. ​(a) How many different selections are possible​?   The 3 cones can be selected in nothing different ways.   ​(b) How many selections contain all green cones​?   There are nothing different selections if all 3 are green cones.   ​(c) How many selections contain 2 green cones and 1 blue cone​?   There are nothing different selections which contain 2 green cones and 1 blue cone.   ​(d) How many selections would include at least 1 blue cone​?   There are nothing different selections which contain at least 1 blue cone

Q: Joe likes to go to an old arcade and play 12 games of Skeeball every day. On​ average, he wins a…

A: In this context, there are fixed number of trials. That is, n = 12. There are two possible outcomes…

Q: There are two players that play a game on an array that consists of 2n numbers. In this game, at…

A: Given: There are two players that plays a game on ana array that consists of2n numbers. In this…

Q: Die A has 4 red and 2 white faces, whereas die B has 2 red and 4 white faces. A fair ped once. If it…

A: (a) Die A has 4 red and 2 white faces. Die B has 2 red and 4 white faces P(head)=P(tail)=1/2 The…

Q: In a game of Jack n Poy, the player that wins 3 times out of 5 games is declared the

A: Given, Players has same chanece of winning. So, p = 0.5 If player wins 3 times out of 5 games is…

Q: 2. In the game of SCRABBLE, you select letters from the group in the pot that are not already on the…

A:

Q: Imagine a two-player game that proceeds as follows. A pot of money is created with $6 in it…

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Q: Amarble is selected at random from a jar containing 2 red marbles, 3 yellow marbles, and 4 green…

A: GivenA jar containsNo.of red marbles=2No.of yellow marbles = 3No.of green marbles = 4Total no.of…

Q: Frank is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6.…

A:

Q: Suppose you play a coin toss game in which you win​ $1 if a head appears and lose​ $1 if a tail…

A: The number of times the head comes is 35 in first 100 tosses, Therefore, the percentage of head…

Q: Suppose a standard​ six-sided die is rolled and you receive ​$1.00 for every dot showing on the top…

A: The expected number of dots is     E(x)=1+2+3+4+5+66       =216       =72       =3.5

Q: You and your team have built a chess computer. To investigate how well it performs, you organise a…

A: Solution

Q: 5. Mr. Bemard and Mr. Meyer go out to lunch and play a game called "One Hundred". Each player puts…

A: The hint helps us develop a strategy for the game and find the guy who ends up winning when both…

Q: Suppose a standard​ six-sided die is rolled and you receive ​$3.00 for every dot showing on the top…

A:

Q: Suppose you play a coin toss game in which you win $1 if a head appears and loses $1 if a tail…

A: As we are authorized to answer only 3 subparts for each question and that you haven't specified…

Q: Keiko is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6.…

A:

Q: Give an example of stable marriage for 3 girls and 3 boys, where nobody gets in couple most…

A: Initialize all men and women to free While there exist a free man M who has still a women  W to…

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A: give: Alice’s claim : New version is better Bob’s claim : Average score is greater than or equal to…

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A: Given query is to find number of meals can be made out of the options.

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Q: A teacher assigns a group of 30 students into 3 groups of 10. The way the assignment process works…

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Q: Assume that the group has a portfolio of 6 stocks. There is 30% chance that any one of these stocks…

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Q: 8 singles, 6 fives, 4 twenties, and 2 hundred dollar bills are all placed in a hat. If a player is…

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Q: Hangman is a paper and pencil guessing game for two players. One player thinks of a word, phrase or…

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Q: Joe likes to go to an old arcade and play 8 games of Skeeball every day. On average, he wins a prize…

A: Given Information:  Win percentage (p) = 0.65  Number of successes (r) = 3  Number of trials (games)…

Q: There are two biscuit tins on a shelf. the red tin contains three chocolate biscuits and seven plain…

A:

Q: A particular two-player game starts with a pile of diamonds and a pile of rubies. On your turn, you…

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A: To Test the null hypothesis that two proportions or binomial parameters are equal. That is, the test…

Q: A certain game involves tossing 3 fair coins, and it pays 11cents for 3 heads , 7 cents for 2 heads,…

A: We can get 3 heads in 3C3=1 way 2 heads in 3C2=3 ways 1 head in 3C1=3 ways 0 head in 3C0=1 way Total…

Q: Q3/ Box contains a lot of lampss if the possibility that a burned lamp is (0-2) and if (4) lamps…

A: Given Data: Let X represent the random variable p=0.2 n=4   X~ Binomial (4, 0.2)

Q: A game known to most children is rock-paper-scissors. On the count of three, each person displays…

A:

Q: 3. Betty is playing a game with a fair die. If she rolls a prime number, she scores 10 times the…

A: here as per your requirement i have calculated Q.3 here fair dice is tossed ,  so total possible…

Q: In a game called NIM, there are two players. At the start, two piles of matches are placed on the…

A: Given information: In the NIM game, two piles of matches are placed on the table each containing two…

Q: A friend of mine is giving a dinner party. His current wine supply includes 7 bottles of zinfandel,…

A: As per guidelines expert have to answer first question three subparts only dear student please…

Q: In a variation of the coin game, there are 22 coins. Two players take turns and take between 1 and 3…

A:

Q: Diana​ Baniak, searching for an Ecology​ class, knows that it must be in one of eight classrooms.…

A: As per given by the question, there are 8 class room and searching for an Ecology​ class from one…

Q: 5. The school has case of 144 donut holes and a case of 24 milks. If these are divided evenly among…

A: 5) As there are 144 donut holes and a case of 24 milks , we need to distribute evenly among the…

Q: The owner of a popular coffee shop believes that customers who drink espresso are less likely to use…

A: X1=15, n1=50, X2=24, n2=50

Q: How much money would you have to lose in order for you average 0 per roll?

A: Here you play a game where you roll 2 six-sided dice. If you roll a 7, you will lose some money, but…

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A: Given data: Total classrooms = 8 4 rooms at random are tried to save time To find:  The possible…

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A:

Q: Suppose there are six blue pens and four red pens in a box. Three pens are drawn from the box…

A: From the given information, Consider, Total pens =10 Total blue pens = 6 Total red pens  = 4

Q: Diana baniak Searching for an ecology class, knows that it must be in one of eight classrooms. Since…

A: We have to find number of ways

Q: Lisa is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6.…

A:

Q: There are 5 white and 3 black balls in the first jar and 4 white and 4 black balls in thesecond jar.…

A: We have to find probability by using basic probability laws.

Q: If they decide to purposely choose 2 of the 22 available dogs rather than randomly choosing any 2,…

A: Formula used: Crn=n!r!n-r!n!=n×n-1×n-2×.…2×1 Here given n=22 and r=2.

Q: Diana Baniak, Searching for an ecology class, know that you must be in one of nine classrooms. Since…

A: We have to find no. Of ways ......

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A: Solution

Q: Suppose that nine children are sitting in a row. When the music starts, they get up and run around…

A: Now suppose that nine children are sitting in a row. When the music starts, they get up and run…

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.