An experiment involves 32 participants. From these, a group of 5 participants is to be tested under a special condition. How many groups of 5 participants are possible?   (b) From a collection of 51 store customers, 2 are to be chosen to receive a special gift. How many groups of 2 customers are possible?

Q: Consider a lottery game that is played by drawing four white balls out of a drum of 59 white balls…

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Q: (a) An experiment involves 30 participants. From these, a group of 4 participants is to be tested…

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Q: 1) Bill is given a jar with eight marbles, six of which are red and two of which are green. Bill…

A: Given: There are 8 marbles : 6 red and 2 green. Bill randomly draws marbles without replacement.

Q: A machine puts out 16 imperfect articles in a sample of 500. After the machine is over-hauled, it…

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Q: A fair coin is tossed 5 times and the sequence of heads and tails is observed. How many outcomes…

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Q: 4. Arranging the possible children of a couple with 3 children given that . second child is a girl.

A: Given:  A couple have 3 children(Boy(B) ,Girl(G))  Then to write sample space 3 children given that…

Q: A bowl contains 10 red balls and 10 blue balls. A woman selects balls at random without looking at…

A: Given: The number of red balls is 10. The number of blue balls is 10. The total number of balls in…

Q: A committee of 4 students is to be made. There are 5 boys and 5 girls available for selection. In…

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Q: 14 ladies of a certain age drop off their red hats at the hat check of a museum. As they are…

A: Given, Total there are 14 hats. We have to determine the ways in which 6 of the ladies recieve their…

Q: A pass code for an account consists of 2 letters followed by 3 symbols. If letters may be chosen…

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Q: 7) Suppose that a class of 20 students is assigned to write an essay. Suppose 4 essays are picked at…

A: Total number of students in class = 20 Number of essays to be picked at random = 4

Q: Twenty people are on a committee, ten women and ten men. Suppose a four-person subcommittee is…

A: From the provided information, Total people = 20 10 men and 10 women.

Q: A fair coin and 2 weighted coins with Pr[H]= 3/4 are in a bag. One is selected at random and then…

A: From the given information, A fair coin and 2 weighted coins are there in a bag. One is selected at…

Q: There are three dice rolled at the same time. b. How many possible outcomes are there if the desired…

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Q: A textbook search committee is considering 12 books for possible adoption. The committee has decided…

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Q: In one question on a history test, a student is asked to match 5 dates with 5 events; each date can…

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Q: In how many different ways can 7 of 19 teachers be selected to assist with the preparation of exams?…

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Q: Suppose we select, without looking, one marble from a bag containing 7 red marbles and 8 green…

A: From the provided information, The bag contains 7 red marbles and 8 green marbles. Total marbles = 7…

Q: An jar contains 4 orange​, 6 ​green, and 3 purple necklace charms. In how many ways can 3 necklace…

A: It is given that the A jar contains 4 orange​, 6 ​green, and 3 purple necklace charms. So that the…

Q: (a) An experiment involves 32 participants. From these, a group of 4 participants is to be tested…

A: Since you have posted multiple question, As per the policy I can solve only first question for you,…

Q: How could you use a​ random-digit generator or​ random-number table to simulate rain if you knew…

A: From the given information, the 50% that it will rain with the conditions we have today.The digits…

Q: Example 44. A committee of 3 experts is to be selected out of a panel of 7 persons; three of them…

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Q: At a baby shower 17 guests are in attendance and 5 of them are randomly selected to receive a door…

A: Combination Rule: The arrangement of r objects from n different objects is given by: nCr=n!r!n-r!

Q: 2. How many different arrangements can be made by using all the letters of the word MATHEMATICS ? 3.…

A: Here use combination

Q: How many possible outcomes for the individual games are there, such that overall player A ends up…

A: From the provided information  Out of the 9 games player A can win any of the 4 games, which gives…

Q: A shipment of 40 computers are unloaded from the van and tested 6 of them are defective In how many…

A: We will find out the required number of ways.

Q: Suppose that there are eight runners in a race. The winner receives a gold medal, the second place…

A: Given Suppose that there are eight runner in a race . The winner receives a gold medal the second…

Q: 6. From a group of 9 men and 5 women, five persons are to be selected to form a committee so that at…

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Q: A bowl contains 10 red balls and 10 blue balls. A person selects balls at random without looking at…

A: No. of Red balls = 10 No. of Blue balls = 10 a) having at least 3 balls of same colour If a person…

Q: Toplay the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying…

A: It is given that a person selected 5 out of 45 numbers. Therefore, the total number of combinations…

Q: a. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? b.…

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Q: n is tossed 4 times, Find out the number of possible outcomes if only one tail will come ou

A: If we toss a fair coin, there are two possible outcomes for each trial that is "Head' and "Tail" .

Q: n order to conduct an​ experiment, 5 subjects are randomly selected from a group of 44 subjects. How…

A: Given data,   Total subjects (n) = 45 Number of subjects that are randomly chosen (r) = 5  How many…

Q: 7. In a chess competition involving some men and women, every player needs to play exactly one game…

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Q: 4. You roll a die with six sides and then you roll a die with 10 sides. How many possible outcomes…

A: Total possible outcomes can be calculated by multiplying the respective possible outcomes of each…

Q: A bowl contains 10 blue balls and 10 green balls. A girl selects balls at random without looking at…

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Q: A student taking an examination is required to answer exactly 10 out of 15 questions. in how many…

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Q: 7. How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 if the…

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Q: A penny is tossed three times and the results heads and tails noted. The process is continued until…

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Q: In a survey, 95% of n = 400 randomly sampled married men said that they would marry their spouses…

A: For men,  = 0.95 * 400 = 380 men were ready to marry there spouses again.

Q: Your field experience instructor wants to line up 9 cars for transportation to a grade school.…

A: Permutation is used to arrange r numbers from n numbers. Combination is used to select the r numbers…

Q: 4. (a) In a group of 8 people, some of them shake hands. Is it possible that everyone shaked hands…

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Q: Suppose we select 2 students randomly from a class of 20 students. The first student  selected will…

A: Given data  There are total of 20 students  We need to select 2 students from them

Q: A pass code for an account consists of 2 letters followed by 3 symbols. If letters may be chosen…

A: Total number of letters available for password, m = 12 Total number of symbols available for…

Q: Random samples of size 3 are drawn from a finite population consisting of the numbers 1,2,3,6,and 8.…

A: A permutation is an arrangement in a definite order of a number of objects taken some or all at a…

Q: If a bank sends a random 5-digit number to customers for security, how many potential numbers are…

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Q: In an experiment, there are 5 possible conditions, and you would like each participant to receive 3…

A: Given information 5 possible conditions Each participant to receive 3 out of 5.

Q: A shipment of 40 computers are unloaded from the van and tested. 6 of them are defective. In how…

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Q: tudents are selected from a group of 13 students for prizes. How many different possible groups…

A: Solution: The students are selected from a group of 13 students  for prizes. To find the different…

Q: how many are the possible cases, regardless of

A: From the given information, The coin is tosses n times. And the coin has two faces.