Some automobiles have four-button locks. To gain entry, push each of the four buttons, in a particular order, to unlock the door. How many different five-digit codes are possible?

Q: The password for a new online gaming site must contain three letters followed by four digits. The…

A: Given that there are 3 letters in the password and the letters can not repeat. There are 26 letters…

Q: You need to create a new passcode for your iPhone, their are 10 numbers to choose from and your…

A: Remark: We know the number of different permutations of n distinct objects taken r at a time is nPr…

Q: the state department of transportation decides to change the plates to have three letters followed…

A: Given query is to find how many plates are possible if three latters followed by two digits.

Q: How many 4 digit house numbers are even? (note: 0351 is not considered a house number).

A:

Q: Walter is creating a 5 digit code for an electronic lock. He can use any number, but cannot use the…

A:

Q: You bought a few packages with the same number of ping pong balls each and then you open all. When…

A: This question is related to numbers and combinations, we will solve it by using given conditions.

Q: iPhones have a 6-digit PIN number, how many different PIN numbers are possible?

A: Choices of filling 6 places are 10 I.e.. 0,1,2,3,4,5,6,7,8,9

Q: The local​ seven-digit telephone numbers in city A have 334 as the first three digits. How many…

A:

Q: In the past, a college required students to use a 4 digit PIN (Personal Identification Number) as…

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: Outside a home, there is an 8-key keypad numbered 1 through 8. The correct five-digit code will open…

A: There are totally 8-key keypad numbers. The correct five-digit code will open the garage door. The…

Q: A fast food restaurant advertises that it offers any combination of 8 condiments on a hamburger,…

A: The number is obtained as follows: The number of choosing none of the condiments on a hamburger:…

Q: The access code to a house's security system consists of seven digits. How many different codes are…

A: Given that the access code to a house's security system consists of seven digits.

Q: Outside a home, there is a 4-key keypad with letters A, B, C, and D that can be used to open the…

A: Given Outside a home , there is a Keypads with letter= A,B,C,D Number of codes=4

Q: From the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9, how many three-digit numbers greater than 400 can be…

A: digits : {1,2,3,4,5,6,7,8,9}  select 3 digits to make 3 digit number.  find no. of ways to make…

Q: Answer the following question. How many license plates are possible if you must have 8 characters,…

A: One of the methods of counting in a problem is the fundamental counting principle. The fundamental…

Q: How many options do you have for a 10-digit password of 26 letters?

A: to find number of option for a 10-digit password of 26 letters

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: If 15 people all shake hands with each other, how many handshakes are there?

A: Number of handshakes = 15C2

Q: The first three digits of a 10-digit phone number make up the area code for the number. How many…

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Q: You have 6 books on a shelf. How many ways could you reorder them? (Enter your answer as a whole…

A: The permutation formula is given by

Q: Outside a home, there is a 5-key keypad with letters A, B, C, D and, E that can be used to open the…

A: 5 key keypad with letter A,B,C,D,E.the key can be used to open the garage if the correct five-letter…

Q: A census taker visited the Jones household, and asked Mrs. Jones for the age of her three sons. Mrs.…

A: After knowing that the ages multiply to 76, here is a complete list of the possibilities:Ages:…

Q: Some automobiles have 4 button locks. To gain entry, push each of the four buttons, in a particular…

A:

Q: Thirty professors gather for a curriculum meeting. How many handshakes will each person make if each…

A: We have given information, Thirty professors gather for a curriculum meeting. i.e. n=30

Q: A license plate is to have the following form: three letters followed by three numbers. An example…

A: There are 26 letters (A-Z) and 10 numbers (0-9) We can pick each letter in 26 ways and we can pick…

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: As I went to pay for my coffee, I saw a sign saying, “Win free coffee for a year! Choose 4 different…

A: The objective of this question is to find out the total number of different 4-digit passcodes that…

Q: Jamal is creating a 5 digit passcode using the digits 0 through 9. How many 5 digit passcodes are…

A:

Q: Ms. Karen has 7 children in her preschool class. She would like to give each student an equal number…

A: Solution is given below:

Q: How many words can be formed from the letters of the word: UNITED

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.