5 numbers are to be chosen from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} How many ways can 5 (not necesarilly distinct) numbers be chosen?

Q: seven prizes are to be given to seven different people in a group of 9. In how many ways can a first…

A: Given, seven prizes are to be given to seven different people in a group of 9. The number of ways =…

Q: How many different passwords of 4 characters can be made using the numbers from 0 to 9 and the…

A: A password of four characters is to be made using the numbers from 0 to 9 i.e. 10 digits and the…

Q: How many symbols of 3 different orders greater than 3 700 can be formed from the set of numbers {…

A: Combination : A combination could be a mathematical technique for scheming the amount of potential…

Q: A restaurant offers a $12 dinner special that has 4 choices for an appetizer, 13 choices for an…

A: It is given that the  A restaurant offers 4 choices for an appetizer, 13 choices for an entree, and…

Q: 2. How many ways can 10 books be arranged in a shelf if one of them is a bible and it must be placed…

A: Given that, 2.  10 books be arranged in a shelf & one of them is a bible and it must be placed…

Q: How many 3 or 4 digit even numbers greater than 700 can be formed by: a. Using the digits 0-9.…

A: EVEN NUMBERS : Even numbers embrace people who conclude in zero,2,4,6, and 8. Even numbers, as an…

Q: HOW MANY WAYS 4 PIZZA TOPPINGS BE SELECTED FROM A CHOICE OF 12 TOPPINGS CAN BE CHOSEN ONLY ONCE?

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Q: Postcodes in a country begin with either 1, 2, 3, 4, 5, 6, 7 or 8 followed by 2 more digits. How…

A: Postcode can start with either 1,2,3,4,5,6,7,or 8 Therefore there are 8 choices for the postcode to…

Q: There are 12 women running in a race. How many different ways   could first, second and third prize…

A: The first winner can occur in 12 ways, the second winner can occur in (12-1)=11 ways, the third…

Q: 5 numbers are to be chosen from {0,1,2,3,4,5,6,7,8,9}. Answer the following questions: 1. How many…

A: Five numbers can be chosen from the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Q: How many three-letter "words" can be made from 4 letters "FGHI" if repetition of letters is allowed…

A: Given that there are four letters FGHI 1) The three-letter words can be made from 4 letters when the…

Q: How many five digits number can be form using the integer 0,1,2,3,4,5,6,7 if  Repetition is allowed…

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Q: Octal numbers are made using the eight digits 0,1,2,3,4,5,6,7. How many octal numbers are 4 digits…

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Q: How many different three digit numbers can be formed using the digits 9,6,7,8,5 and 4 with…

A: Given digits, 9, 6,7,8,5 and 4 Total numbers of given digits = 6

Q: In how many ways can four aces be drawn from a deck of cards.

A: The aim is to find in how many ways four ways can be chosen from a deck of cards. Concepts used: A…

Q: How many three-digit numbers can be formed from the numerals in the set {1, 2, 3, 4} if the…

A: Given digits are 1, 2, 3, 4 i.e, there are 4 different digits

Q: A lottery game requires that 6 different numbers are picked from 1 to 11. If someone picks all 6…

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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: Using the digits 2, 4, 6, 7 and 9, how many five-digit numbers can be formed if the number is…

A: Given Information: Digits = 2, 4, 6, 7 and 9 To find how many five-digit numbers can be formed if…

Q: 2. In how many ways can three numbers be selected from the numbers 1, 2, ... , 300 such that their…

A: This problem is solved using the concept of permutation and combination. please find step by step…

Q: In how many ways can 8 people be seated in 8 adjacent seats in a theater? There are ways to seat 8…

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Q: How many integers between 1 and 1000 are divisible by 3, 5, 11, or 13?

A: We have to find the total  integers between 1 and 1000 are divisible by 3, 5, 11, or 13. First find…

Q: A bank of 9 movies is chosen from for a movie marathon in which 3 movies will be played in a…

A: Given that,  There are 9 movies in the bank. According to the given condition, 3 movies are played…

Q: 2) How many integers between 1 and 200, including both 1 and 200 are divisible by 4 or 5? 3) How…

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Q: Ten prizes are to be given to 10 different people in a group of 16. In how many ways can a first…

A: Given that there are 10 prizes and 16 people.  So the first prize can be given to any of the 16…

Q: Six prizes are to be given to six different people in a group of seventeen. In how many ways can a…

A: Total number of people = 17 Number of prizes to be given = 6 For the first prize, we need to select…

Q: 14 different letters of alphabet are given, words with 6 letters are formed from these given…

A: There are 14 different letters. We will make words with 6 letters.  So there are 146=7529536 ways to…

Q: A four-digit number is to be formed from the digits 0, 1, 2, 3, 5, 7, 8, and 9. How many four-digit…

A: Given,digits is 0,1,2,3,5,7,8,9

Q: A restaurant offers a $12 dinner special that has 4 choices for an appetizer, 11 choices for an…

A: Given data,No of choices for an appetizer=4No of choices for an entree=11No of choices for an…

Q: on a basketball team be filled with 10 In how many ways can 5 starting players (no positions)…

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Q: A license plate consists of   five symbols on each​ plate, where the first two symbols are letters…

A: Fundamental principle of counting : If an event occur in m ways an corresponding to it another event…

Q: How many 3-digit numbers with digits in 1,2,3,4,5,6,7,8,9 (repeats allowed) are divisible by 9

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Q: There are 49 runners in a race. How many ways can the runners finish first, second, and third? There…

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Q: A jersey has two digit number.in how many ways can the number be arranged if 1)No double digit are…

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Q: 4. How many 4-digit numbers that are divisible by 10 can be formed from the numbers 3. 5. 7. 8, 9. 0…

A: Discaimer : 12:31Since you have asked multiple question, we will solve the first question for you.…

Q: A PIN-number for a credit card consists of a sequence of 4 digits chosen from the set…

A: Given the set {0,1,2,3,4,5,6,7,8,9} We find the 4 digits different PIN number

Q: A telephone number consists of 7 digits. How many phone numbers are possible if the first digit is…

A: Solution: The digits other than 4, 3, 2, 1, 0 are 5, 6, 7, 8 and 9.

Q: n crayon box contains 2 green, 3 yellow and 4 blue crayons. In how many ways can one choose 3…

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Q: How many different 3-digit numbers are possible using only the digits 1,5,6,7,8 ? How many…

A: We have to find no of ways for make 3 and 4 digit numbers  when repetition allow and not allowed

Q: How many different license plates are possible if each contains 2 letters (out of the alphabet's 26…

A: Given that license plate contains 2 letters and followed by 5 digits.  There are 26 choices for each…

Q: A committee of 3 is to be formed from a group of 20 people. How many different committee are…

A: A committee of 3 is to be formed from 20 people. So there has to be 3 selections from 20 people…

Q: .76 How many six-digit numbers with different digits belonging to the set ${0,1,2,3,4,5,5}$ and…

A: 6 digit forming a 6 digit number  The total number of 6 digit different numbers = 6!-5! = 720-120 =…

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

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Q: How many three-letter code words can be constructed from the first nine letters of the Greek…

A: 60480 three letter code

Q: How many ways can one select a subset of 10 elements from {1, 2, 3, . . . , 1000} so that the…

A: We use the following summation: Crn+Cr-1=Crn+1nCmm+Cmm+!+Cmm+2+...+Cmn=…

Q: How many different arrangements of 4 letters can be formed if the first letter must be W or K…

A: Total no.of letters(A to Z)=26

Q: 3. Copy Central prints black and white or colored copies. Yesterday, they printed 9 black and white…

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

Q: 5 numbers are to be chosen from {0,1,2,3,4,5,6,7,8,9}{0,1,2,3,4,5,6,7,8,9}. Answer the following…

A: Given sample 0,1,2,3,4,5,6,7,8,9. (1) Possible ways of choosing 5 numbers. Total…

Q: When purchasing a ticket for the PowerBall lottery game a player chooses 5 distinct numbers between…

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Q: There are 54 runners in a race. How many ways can the runners finish first, second, and third? There…

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.