Suppose you break your piggy bank and scoop up a handful of 22 coins (pennies, nickels, dimes and quarters). Prove that you must have at least 6 coins of a single denomination. Suppose you have an odd number of pennies. Prove that you must have an odd number of at least one of the other types of coins. How many coins would you scoop up to be sure that you either had 4 coins that were all the same or 4 coins that were all different. Prove your answer.

Suppose you break your piggy bank and scoop up a handful of 22 coins (pennies, nickels, dimes and quarters). Prove that you must have at least 6 coins of a single denomination. Suppose you have an odd number of pennies. Prove that you must have an odd number of at least one of the other types of coins. How many coins would you scoop up to be sure that you either had 4 coins that were all the same or 4 coins that were all different. Prove your answer.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Suppose you break your piggy bank and scoop up a handful of 22 coins (pennies, nickels, dimes and quarters).

Prove that you must have at least 6 coins of a single denomination.
Suppose you have an odd number of pennies. Prove that you must have an odd number of at least one of the other types of coins.
How many coins would you scoop up to be sure that you either had 4 coins that were all the same or 4 coins that were all different. Prove your answer.

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