In a certain state, license plates each consist of 2 letters followed by 3 digits. How many different license plates are there that have no repeated letters or digits? (Enter the answer without

Q: A state makes license plates with 3 letters followed by 5 numbers. If repetitions are permitted, how…

A:

Q: The seven given numbers are: 5, 6, 3, 4, 1, 2, and 7. A. How many five-digit numbers can be formed…

A: Given seven numbers are5,6,3,4,1,2,7

Q: How many different license plates can be made if each is to display 3 numbers and 3 letters?

A: We have to find out no. Of ways...

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

A:

Q: How many different 4 letter radio station call letters can be formed if the first letter must be W…

A: It is given that, there are for letters and first letter must be W or K.Thus, there are 2…

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

A: Digits: 1, 2, 3, 4, 5, 6, 7.

Q: There are 8 people in a room. Each person shakes hands with each of the other people once and only…

A: Given, There are 8 people in a room. Each person shakes hands with each of the other people once and…

Q: A woman has ten skirts and five blouses. Assuming that they all match, how many different…

A:

Q: When dialing a friend's phone number, a person forgot the last four digits, and only remembers that…

A: The last four places can be taken by any number from 0 to 9. Now, two places have same number.

Q: A license plate consists of 2 letters followed by 4 numbers, and to avoid confusion, the numbers 1…

A: GivenNo.of letters from A-Z =26No.of numbers from 1-0 excluding 1 and 0 = 8

Q: a) How many three-digit numbers less than 700 can be made using the digits 9, 7, 4, and 2? (Each…

A:

Q: In recent years, a state has issued license plates using a combination of two letters of the…

A: Given that, In recent years, a state has issued license plates using a combination of two letters of…

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: Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3…

A:

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: How many 4-digit numbers are there?   And if repetition of digits is not allowed?

A: Given that n= number from 1 to 9 = 9 r = 4 ( since we have to take 4 digit number)

Q: A job interviewer has set 10 questions with four answer options and one correct answer. In how many…

A: The number of ways for two events to occur in a sequence is p×q. Here, p is the number of ways the…

Q: How many 4-letter words can be made from the letters MATH if repetition of letters is allowed?…

A: Given: Letters M , A , T ,H  We need to find number of 4 letter words that can be made.

Q: How many seven digit telephone numbers are possible if the first two digits cannot be twos or zeros?

A:

Q: How many three-letter "words" can be made from 8 letters "FGHIJKLM" if repetition of letters (a) is…

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

Q: From 1, 3, 5, 7, and 9 how many 4-digit numbers can be formed? Note: each digit can be used only…

A: Given ,5 numbers 1,3,5,7,9 respectively. We need to calculate how many four digits number can be…

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: A small town have five police cars: when a call comes in the dispatcher may dispatch no cars, one…

A: Given that there are 5 cars.  The dispatcher may dispatch no cars, one car, two cars, three cars,…

Q: A state makes license plates with two letters followed by four numbers. if no repetitions of the…

A: The license plates must consist of two letters followed by four numbers.

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

A:

Q: In the Americas, automobile license plates contain two letters, followed by four digits. How many…

A: Given,no.of letters=26no.of digits(0 to 9)=10

Q: The park rules require that on duty for every 50 people who visit the parl How many guards should be…

A: The park rules require that one security guard be on duty for every 50 people who visit the park.…

Q: One company’s ID cards consist of 5 letters followed by 2 digits. How many cards can be made if…

A: Consider that there are 26 letters, while the company’s id card consists of 5 letters followed by 2…

Q: Radio stations that are on the west side of a nation have call letters consisting of a K followed by…

A: The first letter is fixed with Z and is then followed by 4 letter( repetition allowed) Then,

Q: A woman has seven skirts and seven blouses. Assuming that they all match, hi combinations can she…

A: Solution:- From given information they are 7 skirts 7 blouses

Q: How many six digit numbers can be formed with no repetitions?

A: We can use all the 6 digits without repetition A 6 digit number cannot have  0 in the first place.…

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: A state makes a license plate with 3 letters followed by 5 numbers. If repetitions are permitted,…

A: To find the different ways in which license plates can be made

Q: A man has eight shirts and three ties. Assuming that they all match, how many different…

A: Given that, Man has 8 shirts and 3 ties How many different combinations can he wear?

Q: How many words, with or without meaning, each of 3 vowels and 3 consonants can be formed from the…

A: Permutation is an arrangement or order of selecting some of the elements from a group or a set of…

Q: In a certain state, all car license plates have four capital letters followed by three digits. How…

A: Given Car license plates have 4 (A to Z) capital letters followed by 3 (0 to 9) digits

Q: How many license plate containing two letter followed by three digit can be formed 2 If the letters…

A: License plate made up of 5 alphanumeric in which first two position taken by letters then last three…

Q: How many different license plates are possible if 2 uppercase letters are followed by 4 digits and…

A: A number plate consist of 2 uppercase letters followed by 4 digits, in which first digit cannot be…

Q: There are 94 people in a​ room, half of whom​ don't speak to the other half. Assume that if they​…

A: Given: Number of people in a room = 94

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: A license plate consists of two letters and three digits. How many different plates can be made if…

A: no.of digits (0 to 9)=10no.of letters (A to Z)=26

Q: A man has eight shirts and five ties. Assuming that they all match, how many different shirt-and-tie…

A: Given,            A man has eight shirts and five ties.

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: In a certain state, license plates each consist of 3 letters from the English alphabet, followed by…

A: There are 26 letters (A-Z) in the English alphabet and 10 digits (0-9).   Use the fundamental…

Q: A girl owns 5 pairs of pants, 5 shirts, 4 ties, and 2 jackets. How many different outfits can the…

A:

Q: A student must answer 7 of the 10 essay questions that are on an exam. How many ways can the student…

A:

Q: How many 3-letter words can be made from the letters MATH if repetition of letters is allowed?…

A: We have given that a four letter word MATH from which we can made 3 letter words in two different…

Q: 2. In a certain country, license plate numbers have 3 letters followed by 3 digits. How many…

A: here use counting principle  for combination  nr = n!(n- r)! r!

Q: There are 125 students in a class. At least how many students came from the same state if there are…

A: There are 125 students and 16 states We divide 125 by 16 to find the least number of students from…

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.