lecture28

# lecture28 - Lecture 28 Counting Announcements Hw7 posted....

This preview shows pages 1–9. Sign up to view the full content.

Lecture 28 Counting

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Announcements Hw7 posted. Due Apr 23. Start early! Final: Wed, May 12, 8am Smith Hall
Basic Counting Principles The product rule Sum rule Inclusion-Exclusion |A| + |B| - |A B|

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Pigeonhole principle If k +1 or more objects (pigeons) are placed into k boxes, then there is at least one box containing two or more of the objects
Generalized pigeonhole principle If N objects are placed into k boxes, then there is at least one box containing N / k objects

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Permutations Permutation of a set S = ordered arrangement of the elements of S Example S={1,2,3} Permutations of S are 1 2 3 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1
r - Permutation r-permutation of S = an ordered arrangement of r elements of S Example S={1,2,3} 2 Permutations of S are 1 2 1 3 2 1 2 3 3 1 3 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
P(n,r) : number of r-permutations of a set with n elements P(n, r) = n (n-1)(n-2)…(n-r+1) = n! / (n-r)! Note: 0! = 1
This is the end of the preview. Sign up to access the rest of the document.

## lecture28 - Lecture 28 Counting Announcements Hw7 posted....

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online