5 numbers are to be chosen from {0,1,2,3,4,5,6,7,8,9}. Answer the following questions: 1. How many ways can 5 (not necessarily distinct) numbers be chosen?   2. How many ways can 5 numbers be chosen if the numbers cannot be repeated?

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: How many two-digit numbers can be formed from the digits 2, 4 and 6 if a. no digit is repeated in…

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Q: In how many ways can 3 red cards be drawn from a standard deck of 52 cards

A: The total number of cards in a deck of cards is 52.

Q: In how many ways can 4 pizza toppings be chosen from 12 available toppings? Your answer is:

A:

Q: 8. Given 1, 2, 3, 4, 5, 6, 7, 0, 9, how many 4-digit numbers can be formed if it must be divisible…

A: We have to solve question number 8

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 ways can 5 bicycles be parked if there are 9 available parking spaces?

A: Number of ways in which 5 bicycles can be parked if there are 9 available parking spaces.

Q: How many different ways a president and a vice president  can be selected from a group of 1414…

A: Total number of candidates = 1414. No. of candidates to be selected =2. Here, while appointing…

Q: How many 4-digit numbers can be formed from 1, 2, 3, 4, and 5 if no repetition is allowed?

A: Given : Numbers = 1,2,3,4 and 5

Q: A four digit number is to be formed from the digits 0, 2, 5, 7, 8. How many numbers can be formed if…

A: 4 ways to fill it (2,5,7,8) 5 ways to fill it (0,2,5,7,8) 5 ways to fill it (0,2,5,7,8) 5 ways to…

Q: In how many ways can 4 pizza toppings be chosen from 12 available toppings?

A:

Q: How many numbers can be formed from the digits 1, 2, 3, and 4 if repetitions are not allowed?

A: How many numbers can be formed from the digits 1, 2, 3, and 4 if repetitions are not allowed.

Q: 4. A chef can prepare 20 different dinners. In how many ways can he select 6 of them for today's…

A: 4. Answer: In 38760 ways can he select 6 of them for today's menu out of 20.

Q: How many ways can 6 ladies be seated in a circular table such that 2 of the ladies must always sit…

A: To find: The number of ways to arrange 6 ladies in a circular table such that 2 of the ladies must…

Q: 9 freshmen, 9 sophomores, 8 juniors, and 7 seniors are eligible to be on a committee. In how many…

A: Solve

Q: how many ways can a coach choose four players from eight bench players to replace four of the five…

A: The number of ways in which r different items can be chosen from n different items is given as Crn…

Q: How many 4-digit numbers can be formed from the digits 1,3,5,6, 8 and 9 if no repetition is allowed

A: Given : No. of digits (N) = 6 Digits : 1 , 3 , 5 , 6 , 8 , 9 4-digit no. can be formed i.e n = 4

Q: In how many ways can 5 people be seated on a sofa, if there are only 3 seats available? * In how…

A:

Q: How many 4-digit numbers can be formed from 0, 1, 3, 5, 7, & 9 if repetition of digits is NOT…

A: Solution-: How many 4-digit numbers can be formed from 0,1,3,5,7 and 9 if repetition of digits is…

Q: In how many ways can you place 9 different books on a shelf if there is space enough for only 5…

A: Given, 9 different books on a shelf and there is space only for 5 books.

Q: In a club with 5 male and 9 female members, how many 5-member committees can be chosen that have at…

A: We have to find no. If ways to arrange.

Q: In how many ways can 9 books be arranged on a shelf if 5 particular books must always stand…

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Q: 4 freshmen and 2 sophomores from a sorority will attend a conference. If the sorority has 14…

A:

Q: How many 4 digits numbers can be formed from digits 1, 2, 3, 4 and 5 if no repetition is allowed and…

A: Answer:  48 Here we want to form a four digit number from 1,2,3,4 and 5 and number should be between…

Q: How many two-digit numbers can be formed from the digits 1, 2, 3, and 4 if a. no digit is repeated…

A: Given that, Digits are given 1, 2, 3 and 4 a) Two-digit numbers with no digit is repeated: Two-digit…

Q: a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit…

A:

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: How many 2 – digit numbers can be formed from the four integers 1, 2, 3, and 4 if repetition is…

A: Given2-digit numbers to be formedNo.of integers =4           (1,2,3,4)

Q: How many five​-digit numbers can be formed with the first two digits odd and the last three digits…

A: The number of digits need to be formed is five. The first two digits are odd and the last three…

Q: How many different three-digit numbers can be formed using the digits 1, 5, 9, 7, 4, 8, and 6…

A:

Q: There are 6 runners in a race. In how many ways can 3 runners finish in first, second, and third to…

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Q: In how many ways can 8 different pizza toppings be chosen from 14 available toppings? There are ways…

A:

Q: 23. How many ways may 5 students be elected from a club with 45 members? 24.How many two-digit…

A: 23) Total number of members = 45 Number of members to be selected = 5 Number of ways the selection…

Q: How many three-digit numbers can be formed from the digits 1, 2, 3, 4, and 5 if repetitions(a) are…

A: To find number of three-digit numbers can be formed from the digits 1, 2, 3, 4 and 5. (a) If…

Q: How many seven-digit numbers can be made from the digits 1 to 9 if repetition is allowed?

A: Given that  To find the number of ways of 7 digit number can be made from the 1 to 9

Q: A group has 12 members. In how many ways can 4 officers consisting of president , vice-president ,…

A: Total members n=12 no of officers r=4 Total no of ways=?

Q: How many different three-digit numbers can be formed using the digits 1, 4, 5, and 9 without…

A: Given N=4 n=3

Q: How many different​ three-digit numbers can be formed using the digits 4, 5, 2, and 8 with​…

A: The given digits 4,5,2,8.  and repetition allowed

Q: How many four digits numbers can be formed from the digits 1 2 3 4 5 6 7 if repetition is not…

A: We have to make four digit numbers without repetition. Here we have 7 digits (1,2,3,4,5,6,7) and we…

Q: How many different 4-digit numbers can be formed from the numbers 2, 4, 5, and 8 if no digit is…

A: How many different 4-digit numbers can be formed from the numbers 2, 4, 5, and 8 if no digit is…

Q: select three (3) coins, but assume that there are 5 dimes, 4 nickels, and 2 quarters. In how many…

A:

Q: Given 9 digits,   1,23,4,5,6,7,8,9, how many 3-digit numbers could be formed without repetition of…

A: Given ,total no.of digits=9 (1 to 9)

Q: 6. From the digits 0, 1, 2, 3, 4, 5 and 6, how many three digits numbers can be performed if no…

A: Given digits are : 0,1,2,3,4,5,6 Total = 7 digits

Q: How many different ways a president and a vice president  can be selected from a group of 14…

A: To find the number of different ways in which a president and a vice president can be selected from…

Q: 9 athletes are to take part in a race. In how many ways can the first 5 places be filled?

A: Given: 9 athletes are to take part in a race To find the number of ways the first 5 places are…

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: In how many ways can 16 different pizza toppings be chosen from 20 available toppings? There are…

A:

Q: How many four-digit numbers can be made from the digits 1 to 6 if repetition is allowed?

A: Number of four digit can be made from digits  1 to 6 :

Q: How many three numbers with no repeated digits, can be formed by the use of the digits 0, 2, 3, 4,…

A: here AS PER GUIDELINES I HAVE CALCULATED 3 SUBPARTS  Three digit number is formed using digit…

Q: How many 7-digit numbers can be made from the digits 1, 2, 3, 4, 5, 6, and 7 if repetition of…

A: Answer: 823543   7-digit numbers can be made from the digits 1,2,3,4,5,6, and 7 if repetition of…

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.