License plate numbers in a certain state consists of seven characters. The first character is a digit (0 through 9). The next four characters are capital letters (A through Z) and the last two characters are digits. Therefore, a license plate number in this state can be any string of the form: Digit-Letter-Letter-Letter-Letter-Digit-Digit (a) How many different license plate numbers are possible? (b) How many license plate numbers are possible if no digit appears more than once? (c) How many license plate numbers are possible if no digit or letter appears more than once?

Q: How many different license plates have the letters J-O in that order?

A: It is given that license plates consist of four digits from 0 to 9 followed by four letters.

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 6-character license plates are possible if the first character must be a letter that is not…

A:

Q: Fifty (50) students in a school played Basketball and Football. Every student plays at least one of…

A:

Q: if these five numbers form a pattern such that the differernce between each pair of numbers is the…

A:

Q: Your friend gives you a list of three five-digit numbers, but she only reveals one digit in each: 3…

A: as we have given three five digit number 3 ? ? ? ?? 8 ? ? ? ? ? 2 ? ? claim- check whether we can…

Q: Suppose that a local area network requires six letters for user names Lower- and uppercase letters…

A: Local arear require six letter for user name & Lower and upper case letters are considered the…

Q: How many different​ 4-letter acronyms can be made if the first letter must be E, X, or P and no…

A: Following solution is provided below

Q: Every Wayne State student has an access id; the 6-character name consisting of 2 letters (a-z)…

A: Students id consists of 6 characters out of which the first two characters are from (a -z) and which…

Q: How many different unique passwords could be made by rearranging the following characters? M A T H E…

A: How many different unique passwords could be made by rearranging the following characters? M A T H E…

Q: How many different ways can six different objects be arranged i

A: Factorial: n!=n*(n-1)*(n-2)*.....*2*1 Given that there are 6 different objects. That is, n=6

Q: Mr. H has a collection of 500 vessels. In how many ways can he name his favorite and second favorite…

A:

Q: The Liberty County Poetry Society awarded 3 different prizes 1 each for 1st, 2nd, and 3rd place…

A: The first prize can be given in 56 ways Second prize in 55 ways Third prize in 54 ways

Q: In choosing what music to play at a charity fund raising event Cory needs to have an equal number of…

A: If an event can be done in n different ways and an other event can be done in m different ways, then…

Q: From a deck of 52 playing cards, 5 cards are to be drawn. How many sets of 5 cards are possible if:…

A:

Q: c) List vertically all the ways each number 0-35 can be represented as a sum of two or more…

A: Assume that limiting the numbers to integers. Let's try a few and see if we can find a pattern:…

Q: A four digit numbers can formed using only the digits 1, 2, 3, 4, 5, 6 (no repeated digits), How…

A: Consider a problem in which there are n vacant inline spots, each of the spots are to be filled by…

Q: You are asked to create a six character password and each character can be any of the 26 letters of…

A: Given: Number of alphabets=26 Number of numerical 2 through 9=8 Total number of characters, n=34 The…

Q: Passwords can have 7 characters. Each character can be an uppercase or lowercase letter, a digit…

A: (a) If any character can be used in any position we have 26 uppercase letters 26 lowercase letters…

Q: How many distinct four-digit numbers can be formed by the digits {1, 2, 3, 4, 5, 5, 5, 8, 6}? Select…

A:

Q: License plates in a certain state start with 3 letters (but they don’t use I or W) and then 3…

A:

Q: Bob owns 13 different books. He wants to pick out and arrange 5 of these books left-to-right on a…

A:

Q: How many different​ 4-letter acronyms can be made if the first letter must be K, U, or Y and no…

A: How many different 4-letter acronyms can be made if the first letter must be K, U, or Yand no letter…

Q: Which of the following situations illustrates combination?

A: Combination is one of the fundamental counting principles.

Q: How many different arrangements can be made using all the letters in CALGARY, if the first letter…

A: CALGARY If the first letter must be G.  Then, Starting with G, need to arrange the remaining 6…

Q: 4.4106 or fuo shep givo blow- 7

A:

Q: You need to choose a new 8-character password for your account. The password can contain only…

A: The objective of this question is to calculate the total number of possible passwords that can be…

Q: How many different 10-letter codes can be made using three a’s, four b’s, and three  c’s?

A:

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

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.