What is the minimum number of cards that must be drawn from an ordinary deck of cards (52) to guarantee that you have been dealt at least three aces (there are 4 aces in each deck)?

Q: How many arrangements are there of the letters of the word MATHEMATICS in which all the vowels…

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Q: How many five-card poker hands containing exactly one pair are possible from a deck of 52 cards?

A: To find n(S), determine the number of ways to choose five-card hands from a pack of 52 cards.…

Q: 5. What is the minimum number of students, each of whom comes from one of the 72 provinces, who must…

A: We have to find What is the minimum number of students, each of whom comes from one of the 72…

Q: Assume that there are 3 pairs of black socks (çorap), 1 pair of pink socks, and 2 pairs of blue…

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Q: A box contain 8 red and 6 green balls. In how many ways can 3 balls be drawn such that 2 is red and…

A: GivenA box containNo.of red balls = 8No.of green balls = 6Total no.of balls = 14

Q: A box contains 18 red, 7 green, 11 blue, 21 yellow and 5 white balls. what is the minimum number of…

A: Given that a box contains 18 red, 7 green, 11 blue, 21 yellow and 5 white balls.

Q: A box contains 15 balls in which seven are green and eight are yellow. If five balls must be drawn…

A: It is given that Number of green balls = 7 Number of yellow balls = 8 Total number of balls = 15…

Q: There are 8 Canadian, 7 German, 6 Chinese, 9 French and 9 Russian students in a class. What is the…

A: Given Data: No. of Canadian=8 No. of German=7 No. of Chinese=6 No. of French=9 No. of Russian=9

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Q: What is the minimum number of students, each of whom comes from one of the 17 regions, who must be…

A: We have students comes from 17 regions.  Now we will distribute no of students to each of 17…

Q: A drawer contains 17 black socks, 17 white socks, 17 blue socks, and 17 brown socks. If the light is…

A: Let’s say that he has picked four socks. If he have already found a pair after two or three or four…

Q: eight are yellow. If five balls must be drawn from the box, in how many ways is this possible if 4.…

A: Given box contains 15 balls. Green balls = 7 Yellow balls = 8 Five balls are drawn from the box.

Q: b . What is the minimum number of cards that must be drawn from an ordinary deck of cards to…

A: b)i) There are 13 ranks. [J,K,Q,A,2,3,4,5,6,7,8,9,10] If we have 2 cards from each rank , then we…

Q: If you put 10 balls randomly into 12 boxes is it guaranteed no box will contain more than one ball?…

A: The number of ways 10 balls can be put into 12 boxes = 12×12×⋯×12 = 1210 Now, the number of ways no…

Q: The gift wrap desk at a large dept. store offers 5 box sizes, 10 wrapping papers, 7 colors of ribbon…

A: To calculate the total number of options for the customer at the gift wrapping counter

Q: Eleven graduate students have applied for two available teaching assistantships. In how many ways…

A: In this problem order for the selection is not mentioned therefore we can use combination for award…

Q: What is the minimal number of people needed in a class to ensure that there are two students with…

A: Given information: To ensure that there are two students with the same birthday (the same month and…

Q: The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee…

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Q: When I arrange the members of a marching band in rows of 2, 3, or 4, there is always 1 person left…

A: To solve the given problem

Q: There are 5 performers who are to present their acts at a variety show. One of them insists on being…

A: We have to solve above question find how many different ways are there to schedule The appearance

Q: What is the minimum number of students, each of whom comes from one of 10 provinces who must be…

A: Let number of students that enrolled = n Number of provinces = 10 Number of pigeon holes = 10 Number…

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: How many subsets with an odd number of elements does a set with 10 elements have?

A: To find the total number of subsets with an odd number of elements of a set with 10 elements, first…

Q: 6. What is the minimum number of students, each of whom comes from one of the 13 states, who must be…

A: Consider there are 13 students those are from each state that enrolled in a university to…

Q: Compute the number of ways to deal a five-card poker hand that has at least one card from each suit,…

A: Given that, Compute the number of ways to deal a five-card poker hand that has at least one card…

Q: There are 9 Canadian, 9 German, 6 Chinese, 9 French and 9 Russian students in a class. What is the…

A: As given that there are 9 Canadian, 9 German, 6 Chinese, 9 French, and 9 Russian students in a…

Q: Find the number of ways of getting at least a pair when randomly getting nine cards from a standard…

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Q: b.How many cards must be selected from a standard deck of 52 cards to guarantee that at least 5…

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Q: Suppose a n × n chessboard is missing two opposite corners. Prove that no matter what n is, you will…

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Q: Compute the number of ways to deal a five-card poker hand that has at least one card from each suit,…

A:

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: What is the minimum number resolution IV? (

A: It is given that here the two-level fractional factorial design is with resolution IV.

Q: Assume the cards are drawn sequentially and without replacement. In how many ways can 3 diamonds be…

A: Given information- We have given that 3 diamonds be drawn from a standard deck of 52 cards. The…

Q: The number of permutations of n items is also called as _______________.

A: The number of permutations of n items is also called as n! (n Factorial).

Q: How many distinct arrangements are possible using the letters of the word POSSIBILITY?

A: Important keys :  When given a number of objects and we would to find the possible different…

Q: Suppose you are asked to arrange 10 books in a shelf. Three of them are Mathematics, 4 are English…

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

Q: 6. How many ways are there to select 3 candidates from 8 equally qualified recent graduates for…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

Q: Find the number of arrangements of the digits {0,1,2,3,4,5,6,7,8,9} such that the first digit is…

A: We need to find the total number of arrangements of digits 0,1,2,3,4,5,6,7,8,9 such that the first…

Q: In a country, there are n farms and in each farm, there are at most 15 types of fruit trees. For any…

A: Use the data given to determine the answer. Use simple mathematics to determine the minimum number…

Q: Colorado consists of 64 counties. What is the minimum number of students, each of whom comes from…

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Q: A box contains 4 black, 2 red and 3 white marbles. In which of the following ways is it correct to…

A: Given: A box contains 4 black, 2 red, and 3 white marbles, and 4 balls are selected from this box. 4…

Q: What is the minimum number of students required in a discrete structures class to be sure that at…

A: As we have five grades: k=5 And the number of students: r=9 And we have to calculate: Nk=r N5=9

Q: 2. In how many ways can five students queue for tickets for a show?

A: The number of ways in which five students queue for tickets for a show is           5!  ways…

Q: Find the minimum number of students that can be admitted to a college so that there are at least 15…

A: Given Data The number of students from one of the 50 states is N=15.   Consider the least 14…

Q: If you have 12 boxes then how many balls do you have to put randomly into the boxes in order to…

A: Given that, We are having 12 boxes. In order to have atleast 4 balls in each box when a random box…

Q: What is the minimum number of students, each of whom comes from one of the 50 states, who must be…

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Q: 2) A class has 25 students. Each day, three students are chosen to present their work at the board.…

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Q: A card game contains 52 cards where 13 are of hearts, 13 are spades, 13 are clubs and 13 are…

A: A combination is a selection of items from a group of items, where the order of selection is not…

Q: In a lottery game, a ticket has a total of 37 numbers to choose from, a player can mark 6 numbers on…

A: Given that, In a lottery game, a ticket has a total of 37 numbers to choose from, a player can mark…

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

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