2) Each type of machine part made in a factory is stamped with a code of the form "letter-digit-digit", where the digits can be repeated. Prove that if 8000 parts are made, then at least four must have the same code stamped on them.

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Q: 1. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?

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Q: How many different binary strings of length 8 are there? How many different binary strings of length…

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Q: Suppose that we have a shipment of 50 microprocessors of which four are defective. In how many ways…

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Q: A passcode is to be created from 2 letters, 2 digits, and 2 special characters (consisting of ?,!,…

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A:

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

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Q: 1. How many different bit strings of length seven are there?

A:

Q: 4. If each Automated Teller Machine card of a certain bank has to have four different digits in its…

A: Answer is mentioned below

Q: How many 6​-letter code words can be formed from the letters O, A, Y, H, K,W if no letter is​…

A: Given: 6 letters = {O, A, Y, H, K, W}

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Q: Show that we can partition 10 people into 5 groups of 2 people each in exactly 945 ways. Justify…

A: We have to prove the given answer.

Q: How many unique codes are possibly formed from two characters, where the first character can be 2 to…

A:

Q: 3) The access code for the safe in my office consists of 4 digits.The first digit must be odd or…

A:

Q: How many strings of eight uppercase English letters are there that start with X, if no letters are…

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Q: A code consists of selecting 3 not-necesarily-distinct digits, followed by a 3-letter "word" chosen…

A: Total ways of selecting 1 Digit: {0,1,2,3,4,5,6,7,8,9} = 10 Letters = {A,B,C,X,Y,Z} = 6

Q: Assume that a password must be at least 8 characters long and include at least 1 digit and at least…

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Q: PLEASE HELP, i really need to understand these questions before my finals. pleaseee?

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Q: A library has 5000 books, and the librarian wants to encode each using a code- word consisting of 3…

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Q: How many three digit passcode can be made from the digits 0-9in the first number is not allowed to…

A:

Q: 2. At a certain company, access codes nust pe 4 composed of the 26 lower case letters of the…

A: Let           A=Access codes 4 to 6 symbolsA1=Access codes with 4 symbolsA2=Access codes with 5…

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Q: 7. How many four-digit codes can be made out of the digits 0, 2, 4, 6, and 8 if repetition of digits…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: A security keypad uses five digits (0 to 9) in a specific order. How many different keypad patterns…

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Q: How many 7-digit ID numbers can be formed if each number starts with 19 and no digit appears more…

A: Solution-: How many 7-digit ID numbers can be drawn formed if each number starts with 19 and no…

Q: How many 4-digit pin codes can be made using the numbers 0 up to 9 if repetition is not allowed and…

A: Solution Total number of digits from 0 to 9 = 10

Q: How many 4-digit codes can be formed from the digits 1,3,5,7, and 9 if repetition of digits is not…

A:

Q: ) How many,8-distinct/digit numbers can be formed if the numbers áre amultiple of/5 and contain the…

A:

Q: Suppose that a password for a locked door must have at least 8 characters, where each character in…

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Q: A 5-digit PIN number is created. The only restriction on this number is that it cannot start with a…

A:

Q: How many people must be selected to guarantee that at least 4 have a birthday in the same month?

A: This is an application of pigeon hole principle. According to pigeon hole principle, if there are n…

Q: 1. A registration code begins with three numbers. If the possible numbers are 1, 2, 7, 9 and 0, how…

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Q: A lock has a code of 3 numbers between 1 and 10. If no numbers in the code are allowed to repeat,…

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

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Q: To gain access to his account, a customer using an automatic teller machine (ATM) must enter a…

A: We will use basic combinatorics.

Q: A security code of four digits from digits 0 to 9 must be entered in a definite order. How many…

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Q: 4. If each Automated Teller Machine card of a certain bank has to have four different digits in its…

A:

Q: (a) How many bit strings of length 8 are there? (b) How many bit strings of length 8 or less are…

A:

Q: How many different ID cards can be made if there are 6 digits on a card and no digur can be used…

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Q: How many 7-digit ID numbers can be made if no digits repeat, and the last digit must be 0 or 1?…

A: Consider the case when the last digit is 0.  The number of digits left is 10-1 = 9 digits.  The…

Q: A computer system allows user IDs that are six characters long. If only alphanumeric characters are…

A: According to the provided data, the user IDs are six, r characters long. The alphanumeric characters…