(b) A certain bank has 31,700 customers. Each customer at the bank has chosen a 4-digit PIN toidentify themselves at the ATM. Examples of PINs are 0678, 2189, 9834. Prove that there is atleast one PIN shared by four or more customers.

Answered: Image /qna-images/answer/7ab87aaf-f7b7-4212-ac64-c1fded1c561d.jpg

Answered: (b) A certain bank has 31,700…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A passcode contains four digits from the digits 0-9. How many different passcodes can be made if no digits is used more than once?
Shannon was born on 02/22/1982. How many eight-digit codes could she make using the digits on her birthday
Compute P9,2. (Enter an exact number.)
A security keypad uses five digits (0 to 9) in a specific order. How many different keypad patterns are possible if the first three digits must be even and the last digit cannot be zero?
A new type of automated teller machine (ATM) requires a five-digit personalidentification number (PIN), using digits 0-9. (The first digit may be 0.) How many suchPINs have no repeated digits?
A 5-digit PIN number is created. The only restriction on this number is that it cannot start with a zero, and it cannot end in an odd digit. There are possible PIN numbers.
A computer program requires the user to enter a 6-digit registration code made up of digits 0,1, 5, 6, 7, and 9. Each number has to be used, and no number can be used more than once. How many different registration codes are possible?
To use an automated teller machine at a certain bank, you must enter a 5-digit code, using the digits 1–9. How many 5-digit codes are possible if repetition of digits is permitted?
A standard-issue 2020 New Jersey license plate had one letter, then two digits, followed by three letters. New Jersey DOO SPA Garden State These plates were not allowed to have letters D, T, or X in the fourth position, or the letters I, O, or Q in any position. With these restrictions, how many different license plates were possible in 2020?
A website instructs users to create a password using 44 alphanumeric characters (letters or digits). Capitalization doesn't matter. How many such passwords are possible that do not repeat any characters?
A user's password to access a computer system consists of three letters followed by two digits. With only lowercase letters, there are 263 * 102 passwords. How many different passwords are possible if uppercase and lowercase letters are distinguished?
A corporate ID number consists of any three numerical digits, followed by any two letters of the alphabet, followed by four more digits. How many different ID numbers are possible?

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

(b) A certain bank has 31,700 customers. Each customer at the bank has chosen a 4-digit PIN to identify themselves at the ATM. Examples of PINs are 0678, 2189, 9834. Prove that there is at least one PIN shared by four or more customers.