Chapter 6: Q25E (page 430)
Show that and are logically equivalent
logically equivalent.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
How many different permutations are there of the set {a,b,c,d,e,f,g} ?
a) Explain how to find a formula for the number of ways to select robjects from nobjects when repetition is allowed and order does not matter.
b) How many ways are there to select a dozen objects from among objects of five different types if objects of the same type are indistinguishable?
c) How many ways are there to select a dozen objects from these five different types if there must be at least three objects of the first type?
d) How many ways are there to select a dozen objects from these five different types if there cannot be more than four objects of the first type?
e) How many ways are there to select a dozen objects from these five different types if there must be at least two objects of the first type, but no more than three objects of the second type?
12. How many different combinations of pennies, nickels, dimes, quarters, and half dollars can a piggy bank contain if it has 20 coins in it?
Find the coefficient of.
Give a combinatorial proof that\(\sum\limits_{k = 1}^n k \cdot {\left( {\begin{array}{*{20}{l}}n\\k\end{array}} \right)^2} = n \cdot \left( {\begin{array}{*{20}{c}}{2n - 1}\\{n - 1}\end{array}} \right)\). (Hint: Count in two ways the number of ways to select a committee, with\(n\)members from a group of\(n\)mathematics professors and\(n\)computer science professors, such that the chairperson of the committee is a mathematics professor.)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
