A license plate consists of 2 letters followed by 4 numbers, and to avoid confusion, the numbers 1 and 0 are not used. How many different license plates are possible? How many plates are possible if repetition is not allowed?

Q: In how many ways can 2 pizza toppings be chosen from 12 available toppings? Your answer is :

A: Consider the formula for the n objects taken r at a time is, Cn,r=n!r!n-r! Then, the number of ways…

Q: How many license plates can we have of three digits followed by three letters? We allow repeated…

A: Since, there are 10 possible digits for the numbers (0 to 9), and 26 possible letters (A to Z). As,…

Q: Standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed…

A: we know thatno.of letters (A to Z)=26no.of digits(0 to 1)=10

Q: A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without​ looking, how many…

A: Given: There are total 4 oranges, thus it is not possible to get 5 oranges.

Q: 4. Credit cards and debit cards often require a PIN number consisting of 4 digits. Wanda wants to…

A:

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

A:

Q: In how many ways can 10 people be seated on a bench if only 4 seats are available?

A: Given problem Given that   In how many ways can 10 people be seated on a bench if only 4 seats are…

Q: A clothing store has a selection of 80 different ties. How many ways can six ties be selected for…

A: It is given that, A clothing store has a selection of 80 different ties. Chris and Alex select 6…

Q: How many 5 letter "words" can be formed if exactly 2 of the letters are vowels if repetition is…

A:

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

A:

Q: How many ways are there to pick three dipping sauces, if you can pick three of the same?

A:

Q: a family wants to adopt 2 cats and 3 dogs from a shelter that has 12 cats and 15 dogs. in how many…

A: The number of ways of selecting 2 cats from 12 cats is,

Q: Of 10 possible books, you plan to take 4 with you on vacation. How many different collections of 4…

A:

Q: A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many…

A:

Q: A man has 3 different pairs of shoes, 8 different pairs of socks, 4 different pairs of slacks, and 2…

A: We have given that 3 different pairs of shoes 8 different pairs of socks  4 different pairs of…

Q: A New club at Arvin High has 22 members. In how many ways can the club elect a president and Vice…

A: The number of members in the club is 22. The number of ways of electing a president is C122=22.…

Q: How many ways can Marie choose 22 pizza toppings from a menu of 66 toppings if each topping can only…

A: Note: Thank you for the question. The question is considered as choosing 2 pizza toppings from a…

Q: A student club consists of 10 freshmen and 8 sophomores. How many different four-person committees…

A: A student club consists of 10 freshmen and 8 sophomores.

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

A: To find the number of ways

Q: In how many ways can 7 people be seated on a sofa if it can only accommodate 5 people?

A:

Q: There are 58 members on the board of directors for a certain non-profit institution. If they must…

A: Given that,There are 58 members on the board of directors.

Q: How many possible lock codes are there if repetition of letters and numbers is not allowed?

A:

Q: password contains 2 letters and 2 digits.  How many passwords are possible if repetitions are NOT…

A: The number of letters is 2 and the number of words is 2.

Q: The board of directors corporation must select a president, secretary, and a treasurer. In how many…

A: Given Data: The total number of members is: n=25 There are three members required a president,…

Q: How many 5-number license plates can be made using the digits: 0, 1, 2, 3, 4, 5, if repetitions are…

A: Given that 5-number license plates that are made using digits 0, 1, 2, 3, 4, 5. We have to determine…

Q: Certain automobile license plates consist of a sequence of three letters followed by four digits. If…

A: We have a license plate that consists of a sequence of three letters followed by four digits. The…

Q: There are 55 members on the board of directors for a certain non-profit institution. If they must…

A:

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: How many different ways can a visiting nurse visit  9  patients if she wants to visit them all in…

A: number of patients n=9   Different number of ways that n different items can be arranged is n!…

Q: If repetitions are not permitted, from the 6 digits 0, 2, 3, 4, 5, and 8, how many 4- digit number…

A:

Q: Customer account "numbers" for a certain company consist of 4 letters followed by 4 numbers. How…

A: There are 26 alphabet and the Digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The number of different…

Q: In a music club with 15 members, 7 people played the piano, 11 people played the guitar, and 2…

A: Given that in a music club of 15 members 7 people played the piano, 11 people played the guitar and…

Q: Two cards are chosen from a 52-card deck, how many ways can 2 Queens be choser

A: There are total of 4 queens in the deck of 52 cards.  We need to choose 2 queens .

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 4 shirts, 4 pairs of trousers, 3 pairs of socks and 2 pairs of shoes. How many different…

A: Given Number of shirts = 4 Number of trousers = 4 Number of pair of socks = 3 Number of pair of…

Q: Standard automobile license plates in a country display 1 numbers, followed by 2 letters, followed…

A: The number of numbers from 0 to 9 is 10 and the number of letters is A-Z is 26.

Q: There are 4 different Mathematics books and 5 different Science books. In how many ways can the…

A:

Q: A dance club needs 3 new members. If there are 5 males and 9 females applicants, in how many ways…

A: Solution

Q: For a Halloween party, each guest can choose from the 6 different kinds of candy to have in a prize…

A: Given,no.of different kinds of candy=8

Q: Eight runners are hoping to take part in a race, but the track has only six lanes. In how many ways…

A:

Q: Standard automobile license plates in a country display 3 numbers, followed by 2 letters, followed…

A:

Q: If you pick 4 cards without replacement from a standard deck of 52 cards, how many different…

A:

Q: The board of directors of a corporation must select a president, a secretary, and a treasurer. In…

A:

Q: A book club offers a choice of 5 novels from a list of 10. How many 5-novel selections can be made?

A: Given data: The total numbers of books are n=10. The numbers of novels selected are x=5.

Q: Two freshmen and three sophomores from a sorority will attend a conference. If the sorority has 12…

A:

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…

Q: How many ways are there to seat 6 different boys and 6 different girls along one side of a long…

A: Given that, there are 12 persons and 12 seats. 12 persons includes 6 boys and 6 girls. Therefore,…

Q: As a television executive, you have been given 8 shows to choose from to run during your prime time…

A: Total number of shows available = 8 Available time slot = 6

Q: If a club consists of 12 members, how many different ways are there for the club to fill the…

A: Given,total members=12