Serial numbers for a product are to be made using 2 letters followed by 2 digits. The letters are to be taken from the first 6 letters of the alphabet, with no repeats. The digits are taken from the 10 digits (0, 1, 2, ..., 9), with no repeats. How many serial numbers can be generated?

Q: 3) Sarah writes down random positive integers when she gets bored. Prove that if Sarah writes 1001…

A: Given:  Sarah writes 1001 numbers.  Since there are 10 digits, i.e., there are only 103 = 1000…

Q: 23. How many even three digit numbers greater than 400 can be formed from 1, 2, 3, 4, 5, 6, 7, 8,…

A: Given that, 23. How many even three digit numbers greater than 400 can be formed from 1, 2, 3, 4, 5,…

Q: 1. How many three digit numbers can be formed from the digits 1,2,3,4 and 5 if one is not to used as…

A:

Q: Give a formula for the number of permutations of [n] with no cycles of length exactly 2. Your…

A: Formula for the number of permutations of [n] with no cycles of length exactly 2 is derived.

Q: A stack of 10 cards numbered 0, 1, 2,.....,9 in some order lies face up on a desk. form a new stack…

A: Given: There is a stack of 10 cards numbered 0, 1, 2,.....,9 in some order lying face up on a desk.…

Q: Find S, the sum of first 15 Natural numbers 15

A: We have to find sum of first 15 Natural numbers.   S15? Solution :  As we know that the sum of first…

Q: How many four-digit serial numbers can be formed if no digit is to be repeated within any one number…

A: For the first digit, we have 9 choices. From 1 to 9.  For the second digit, we have 9 choices. Any…

Q: A code have 4 digits in a specific order. The digits are between 0-9. How many different…

A: Code = 4 digits No. of available digit = 10 Repetition = not allowed Order is important, so we will…

Q: Suppose each license plate in a certain state has three letters followed by three digits. The…

A: * License plate must have       3 letters and 3 digits ; repetitions allowed.Also , letters H and L…

Q: 1. How many 3 or 4 digit even numbers greater than 700 can be formed by: a. Using the digits 0-9.…

A: Let there are three chairs A, B and C in one side of a table. The different ways in which these…

Q: How many four-digit combinations can be formed using digits 0 to 9?

A: Total number of digits n=10 Number of digits for combination r=4

Q: Suppose each license plate in a certain state has two digits, followed by two letters, followed by…

A: Given that the license plate has two digits followed by two letters again followed by two digits. Q…

Q: How many even 4-digit numbers can be formed from the digits 1, 2, 6, 7, and 9 with no repetitions…

A: There is no repetition allowed.. At unit place we have two choices 2 or 6 In 10th place we have…

Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: How many different ways can you arrange 2 letters from a set of 3 letters {T, S, U} such that…

A:

Q: 2. even numbers are in their natural positions. Determine the number of permutations of {1, 2, 3, 4,…

A: Here we use combination rules. And set theoretic rules.

Q: Compute the number of ways we can select n fruits from 4 types of fruit (assume an unlimited supply…

A: Given Number of apples is even Number of bananas is a multiple of 5 Find The number of ways we can…

Q: A) How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Note :- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Assuming that any arrangement of letters forms a 'word', how many 'words' of any length can be…

A:

Q: A four digit marathon race number is generated using only the digits 0, 1, 2, 3, 4, 5.  If…

A: We need four-digit race number and each place can be filled by 0, 1, 2, 3, 4, & 5

Q: 1. Suppose a company has hired ten new employees every Monday since it began. Each new employee…

A: I) There is 4 Mondays in a month. Total number of Mondays till the first Monday of the 18th…

Q: How many combinations are there to pick r objects from 2n objects numbered from 1 to 2n with n > 2…

A:

Q: How many 5-digit license plate numbers can we generate from the numbers, 0, 1, 2, 3, and 4 if it…

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A: When the repetition is allowed in formation the general formula for calculating the possibility is…

Q: Suppose each license plate in a certain state has two digits, followed by two letters, followed by…

A: To understood this, consider a problem in which there are r vacant inline spots, each of the spots…

Q: Use permutations to solve. From a cooler with 9 different kinds of soda, 3 are selected for 3…

A: The formula of permutation is: Prn=n!n-r! This is the required answer.

Q: A lottery game requires that you pick 7 different numbers from 1 to 77. If you pick all 7 winning…

A: We have to find the no  of ways given as:

Q: how many six-digit numbers can be formed so that 2 are in the place of thousandth and 5 in the place…

A: First number can not be 0. So we can pick the first number in 9 ways. (1 to 9)

Q: Suppose each license plate in a certain state has three digits followed by three letters. The digits…

A:

Q: ) How many 4 digit numbers that are divisible by 10 can be formed from the numbers 3, 5, 7, 8, 9, 0…

A:

Q: A1. How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Since you've asked multiple parts questions, as per our answering guidelines we are supposed to…

Q: set of two - digit numbers obtained from the digits 1

A:

Q: 1. How many 3-digit numbers can be forms from the four digits 0,1,2,3 if: a) no two digits are to be…

A: according to our guidelines we can answer only three subparts, or any question and rest can be…

Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A: There are 6 positions in the license plate that need to be filled. Out of these 6, first 4 positions…

Q: Number of circular permutations of different .!things taken all at a time is (n-1)

A:

Q: How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never there in the…

A:

Q: Suppose each license plate in a certain state has one digit, followed by four letters, followed by…

A: FORMAT of number = 9AAAA9 (1 number, 4 letters, 1 number) A license plate has six spaces to be…

Q: Fermat's theorem is true for only prime number. إختر واحداً.

A:

Q: (a) How many permutations of (10] are there that EITHER alternate even and odd numbers or have even…

A: Let consider the permutations of 10 as the ordering of  the elements of 10 rather than as an…

Q: How many 5-number license plates can be made using the digits 1,2,3,4,5,6,7, if an odd digit must…

A: Given Data: The total number of digits available is: n=7 The numbers required on number plate is:…

Q: . Find the number of permutations of the letters of the word ‘REMAINS’ such that the vowels always…

A: We can solve these questions using given details

Q: 5. Prove that the sum of a two digit number and its reversal is a multiple of 11.

A:

Q: 5. Suppose we have an enumeration of A ao, a1, A2, ·.. (1) without repetitions (i.e., all the a; are…

A:

Q: 4. A password to a vault must have at least 8 characters where each character can be an English…

A: It is given that password can be  English letter or a digit. So available characters are:…

Q: face the top card face up in your hand place the second card faceup under the first card place the…

A: Given,  A stack of 10 cards numbered 0,1,2,3...9 in some order lies face up on a desk form a new…

Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A:

Q: Serial numbers for a product are made using 3 letters followed by 2 numbers. If the letters are…

A:

Q: A man finished a job in 5 days. On the first day, he finished 1/m of the job. On the second day, he…

A: Given - A man finished a job in 5 days. On the first day, he finished 1/m of the job. On the second…

Q: Suppose each license plate in a certain state has one digit, followed by four letters, followed by…

A: Given, Each license plate in a certain state has one digit followed by four letters followed by one…

Q: A pizza chain wants to send codes for $2 off a large pizza to the subscribers of its e-mail list.…

A: Given that there are 3 positions for letters. Each position can have 23 choices. So the total…

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.