Assume you are rolling two​ dice; the first one is​ red, and the second is green. Use a systematic listing to determine the number of ways you can roll a total less than 10 on the two dice.   In how many ways can you roll less than 10​?

Q: How many different 5-letter words can be made a. if the first letter must be C, Z, T, or L and no…

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Q: In a shipment of 10 items where 3 are defective. In how many ways can you receive 4 items where 2…

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Q: A company received a shipment of 41 laser printers, including 8 that are defective. 3 of these…

A: Given that , A company received a shipment of 41 laser printers   i.e. Number of sample space = S =…

Q: Given 25 patients with known cancer, how many will have negative test? Given 50 patients in good…

A: Here AS PER POLICY I HAVE CALCULATED 3 SUBPARTS PLZ REPOST FOR REMAINING PARTS  Here given 80%…

Q: How many possible results are there that A finished the first, B finished the second, and C finished…

A: SIX STUDENTS ARE SELECTED TO RUN 100 METER SPRINT. ASSUME THAT THEY ARE EQUALLY GOOD AND RESULT ARE…

Q: There are 12 athletes joining the Baguio Marathon Event. How many ways can the first, second, and…

A: Given that: There are 12 athletes joining the Baguio Marathon Event.  Tolat people = 12 By using…

Q: Suppose 15 cars start at a car race. In how many ways can the top 3 cars finish the​ race? The…

A: Permutations: The number of permutations of r items selected from n items is, Prn=n!n-r! In this…

Q: A man is dealt a poker hand (5 cards) from an ordinary playing deck. In how many ways can be dealt a…

A: Given problem Given that   A man is dealt a poker hand ( 5 cards ) from an ordinary playing deck.…

Q: In how many ways can you seat 12 people at two round tables with 6 places each? Think of possible…

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Q: A  box contains 8 ten-peso coins and 5 five-peso coins. In how many ways can 3 coins be drawn in…

A: a) The formula for combination is nCr= n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)] / r!.…

Q: 10 samples of different cakes are on display as customers leave a store, they are told that they can…

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Q: Three cards are chosen without replacement from a deck of 52 cards and placed in order from first to…

A: In the deck of 52 cards, there are total 4 6's. (One for each of hearts, diamonds, spades and clubs)…

Q: USA Today reported that about 20% of all people in the United States are illiterate. Suppose you…

A: c. Obtain the number of people who are interviewed is 87% certain that at least 7 people are…

Q: Find the number of different ways to draw a 5-card hand from a standard deck (four suits with 13…

A: Solution : Find the number of different ways to draw a 5-card hand from a standard deck  of cards to…

Q: In how many ways can a coach choose three swimmers from among five swimmers? Combination O Not…

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Q: 6. The University of Montana ski team has 15 entrants in a men's downhill ski event. The coach would…

A: 6) The number of entrants in men’s downhill ski event is 15.

Q: In how many ways can we of 12, of which a particula included? a. 904

A: Topic:- permutation and combinations

Q: How many combinations are possible? Assume the items are distinct. 9 items chosen 4 at a time…

A: Combinations: The number of combinations of r items selected from n items is, nr=n!n-r!r! It is…

Q: Consider the letters a, b, c, d, & e .  In how many different ways can three letters be selected and…

A: Consider the letters a, b, c, d, & e Total 5 letter  ways to select three letter will be 5C3 =…

Q: 5. Dertemine if the improper in

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Q: a. In how many ways can the three-grill displays be selected from the 5 displays?

A: Given that  Number of different displays (n) = 5 But, Only three would be selected . Number of…

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: 4. Find the number of different ways that a family of 6 can be seated around a circular table with 6…

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Q: how many arrangements of the letters from the word COUNTING begin with a vowel

A: C = 1  O = 1 U = 1 N = 2 T = 1 I = 1 G = 1 __________________ Total = 8 __________________ Vowels =…

Q: How many ways 5 students be seated in a row of 5 chairs for a pictorial?

A: Given students=5 chairs= 5

Q: How many words can be formed by permutation of the letters of the word DEPRESSION such that each…

A: Given word DEPRESSION We have to calculate No. Of words such that obtained word does not contain 2…

Q: in how many different ways could Dopey not be between Grumpy or Sleepy

A: Grumpy is second from the right and Sleepy is third from the left. Total positions where Dopey can…

Q: Arestaurant offers a 512 dinner special that has 5 choices for an appetizer, 11 choices for an…

A: Given information 5 choices for appetizer 11 choices for an entrée 3 choices for desert

Q: In how many ways can first, second, and third prizes be awarded in a contest with 840 contestants?…

A: We have to find number of ways to distribute the awards.

Q: In how many ways can a person invite 4 out of their 13 closest friends to a dinner party?

A: Here there are 13 friends out of which the person has to invite 4 friends for the dinner party. Here…

Q: 12 In how many ways can a starting line up composed of 5 players be selected from a team with 14…

A: It is given that n=14 and r=5.

Q: How many 3-digit numbers with no repeated didgits using 4,5,6,7,8 can be a) Less than 520 b) Greater…

A: (a)given digits are 4,5,6,7,8.     Number of digits = 5 ; for the formation of 3 digit numbers from…

Q: In how many ways can first, second, and third prizes be awarded in a contest with 720 contestants?…

A: We have given that- We have to award first, second, and third prizes in a contest with 720…

Q: Consider a shipment of 50 laptops of which four are defective. A. In how many ways can we select…

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Q: In how many ways can 5 students line up for a registration?

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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: Los Angeles Dodgers. From the official website of the 2013 Los Angeles Dodgers major league baseball…

A: Given info:Five active players available on roster to play outfield.

Q: ny three-letter "words" can be made from 6 different letters "FGHIJK" if... a) Repetition of…

A: The fundamental counting principle says that if n ways are there to complete one thing, and m ways…

Q: In how many ways can 9 member of the family be seated in a round table with 7 chairs?

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Q: Arestaurant offers a $12 dinner special that has 5 choices for an appetizer, 11 choices for an…

A: Number of different ways to choosen r items from n items  =ncr

Q: How many words can be formed by permutation of the letters of the word DEPRESSION such that each…

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Q: In how many ways can three hearts be drawn from a deck of cards? (Order is not important.) _____…

A: Given: There are 13 hearts in total

Q: For n attributes A,, A2, --. , An (A, A2 . An) 2 (A,) + (A2) + .. + (A,)- (n - 1)N Where N is the…

A: To show that, For n attributes A1, A2,..... , An. (A1, A2,..... , An) ≥ (A1)+(A2)+...+(An)-(n-1)N…

Q: How many three-letter words (with or without meaning, without repetition of letters) are formed with…

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Q: In how many ways can a group of 5 students be picked from a class of 14 students to represent the…

A: There are total 14 students.  We will pick a group of 5 students from them.   Since it is a group,…

Q: Owners of a restaurant advertise that they offer 1,114,095 different lunches based on the fact that…

A: To explain: How the owner of a restaurant arrive to the number 1,114,095. Given: The owner have 16…

Q: Two cards are drawn in succession and in without replacement from a set of 12 cards. How many sets…

A: Permutation:         The act of arranging the members of a set into an order or sequence, if it is…

Q: How many three-letter words (with or without meaning, without repetition of letters) are formed with…

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Q: How many different ID cards can be made if there are 6 digits on a card and no digur can be used…

A: Given: Number of digits = 6 No digits is used more than once.

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.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.