Your school locker has a dial with 50 numbers which required 3 numbers to open.  (It is not a combination lock.)  IF the numbers CANNOT be repeated, which expression would give you the number of possible 'combinations' (permutations)?

Q: You need to choose 4 random digits to create a 4-digit code for the lock on the safe. 0000 and…

A: The lock consist of 4 digit code 1st 2nd 3rd 4th The first place can be filled in 10 ways by…

Q: ou have 4 different russian books, 5 different french books, and 6 different spanish books, in how…

A: You have : 4 different Russian books (R) 5 different French books, and (F) 6 different Spanish books…

Q: How many three-number combinations are possible on a combination lock having 40 numbers on its dial…

A: We have , total 40 number on dial and we have to find the combination lock of 3 digits. Since , the…

Q: A Zoom class has 48 students, and for an in-class activity they will be going into breakout rooms in…

A: a) The number of different breakout room assignments if the breakout room numbers matters is,…

Q: Find the number of way to arrange the letters in the word ESTRENGENT. if identical letters must be…

A:

Q: A combination lock uses 3 numbers, each of which can be 0 to 23. If there are no restrictions on the…

A:

Q: How many ways are there to deal hands from a standard playing deck to four players if: 1. Each…

A: Consider the provided question, Given, 4 players are playing cards. (1) The number of ways each…

Q: A license plate is to consist of 4 digits followed by 2  uppercase letters. Determine the number of…

A: Solution-: Given: A license plate is to consist of 4 digits followed by 2  uppercase letters. We…

Q: A particular online game requires that you create a 6 digit number. The only digits available are…

A: Concept:

Q: To use an automated teller machine at a certain​ bank, you must enter a 3​-digit ​code, using the…

A: Given information:The number of possible 3-digit code has to be computed where repetition of digits…

Q: As the project manager of a project, you are in charge of a team of seven people which includes…

A:

Q: A combination lock uses 4 numbers, each of which can be 0 to 26. If there are no restrictions on the…

A:

Q: A combination lock uses 3 numbers, each of which can be 0 to 31. If there are no restrictions on the…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters (a) is…

A: Given5 letters is "FGHIJ"No.of letters = 5

Q: How many four-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9 (a) if each digit…

A: We have to find total number of four-digit numbers :

Q: How many three-letter "words" can be made from 10 letters "FGHIJKLMNO" if repetition of letters (a)…

A: Solution: 39. From the given information, the 10 letters are “FGHIJKLMNO”.

Q: Your school locker has a dial with 50 numbers which required 3 numbers to open.  (It is not a…

A: There are 50 combination lock. Once a number is chosen it can not be chosen again. So, the number of…

Q: From the deck of 52 playing cards, how many ways can 2 cards be drawn such that one is face card and…

A:

Q: The employees of a company are given a 4-digit identification number. How many different numbers are…

A: GivenThe employees of a company are given a 4-digit identification numberNo.of digits from 0-9=10

Q: How many 4-digit odd numbers can be made from the digits 0; 2; 4; 5; 8; 9 if the number has no…

A:

Q: Suppose that you have a combination lock that uses letters instead of numbers for its combination,…

A: Solution: The total number of letters is 26 and the lock will be opened with four letters and…

Q: How many three-letter "words" can be made from 9 letters FGHIJKLMN'' if repetition of letters (a) is…

A: Permutation: It defines the number of possible ways an object can be arranged or ordered. The…

Q: A combination lock uses 3 numbers, each of which can be 0 to 33. If there are no restrictions on the…

A:

Q: A combination lock uses 4 numbers, each of which can be 0 to 24. If there are no restrictions on the…

A: Given information- We have given that a combination lock uses 4 numbers, each of which can be 0 to…

Q: How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters (a) is…

A:

Q: If I am creating a 5-digit number combination, how many combinations will be created if the first…

A:

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 distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2 orange marbles…

A: Given problem:- How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2…

Q: A combination lock uses 3 numbers, each of which can be 0 to 38. If there are no restrictions on the…

A:

Q: A combination lock uses 4 numbers, each of which can be 0 to 36. If there are no restrictions on the…

A: Here, it can be observed that all numbers are independent of each other.

Q: A teacher wants to assign 4 different tasks to her 4 students. In how many possible ways can she do…

A: To know how many possible ways can a teacher assign 4 different task to her student, we must use the…

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 three-letter "words" can be made from 6 letters "FGHIJK" if repetition of letters (a) is…

A: Given 6 letters is "FGHIJK"

Q: Your friend hands you his iPhone and wants you to attempt to unlock it on the first try. How many…

A:

Q: How many four digit codes can be made out of the digits 0,2,4and 8 if the repetition of digits is…

A: We have to find four digit codes can be made out of the digits 0,2,4and 8 ....

Q: A computer password is to consist of three lower case letters followed by two digits. Determine how…

A:

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 three-letter "words" can be made from 10 letters "FGHIJKLMNO" if repetition of letters (a)…

A: Without Repetition : The number of ways to draw a 'r' units from 'N' population of units by using…

Q: To gain access to his account, a customer using an automatic teller machine (ATM) must enter a…

A: We will use basic combinatorics.

Q: To use an automated teller machine at a certain​ bank, you must enter a 5​-digit ​code, using the…

A: You can choose 1st digit in 9 ways.  For each of these 9 ways you can choose 2nd digit in 9 ways as…

Q: If radio station call letters must begin with either K or W and must include either two or three…

A: Given: Total letters = 26

Q: * For the first four letters in the English alphabet, a. list the possible permutations of three…

A: (a)Here, order matters. Therefore permutation rule can be applied.

Q: How many four-digit numbers can be formed from the numbers 1, 3, 4, 6, 8, and 9 if repetition of…

A:

Q: Suppose your school has 1000 students. Why can you be pretty sure that some pair of them will have…

A: Given that there are 1000 students in school. We need to check if there are some pair of students…

Q: A large corporation is concerned with security and identity theft.  So, instead of using workers’…

A: Topic = Permutation and combination

Q: How many ways can four of the letters of the word MAILBOX be selected and written in a row if the…

A:

Q: A witness to a hit-and-run accident tells the police that the license plate of the car in the…

A: The first letter has only one(A) chance, the second letter has 26 ways, the third letter has 26…

Q: In Yoongi’s drawer, there are 7 identical pairs of brown socks and 9 identical pairs of green socks.…

A:

Q: A combination lock uses 4 numbers, each of which can be 0 to 27. If there are no restrictions on the…

A:

Q: How many three-letter "words" can be made from 7 letters "FGHIJKL" if repetition of letter (a) is…

A: The given letters are FGHIJKL are have to find the no of three letterwords can be formed if…

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.