# 15_Counting - Permutations An ordered arrangement of r...

This preview shows pages 1–7. Sign up to view the full content.

Permutations 10/13/11 An ordered arrangement of r elements out of n distinct elements is called an r-permutation. For the above problem, we counted 3-permutations of 3 distinct elements: Example : If the number of available students is 5 and the line should have three students, then the number of ways to form a line is

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

View Full Document
right hand side Example : How many ways are there to select three -- first, second, third place -- winners out of 100? Problem 2 . S={a,b,c,d,e,f,g}. |S|=7.
2'. Example 7 . How many ways can the letters A, B, C, D, E, F, G, H be permuted to form 8-letter strings that contain the substring ABC. Alternate solution:

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

View Full Document
Combinations
Theorem 2 An r-combination of the elements of a set is an unordered selection of r elements from the Set. Example 11 . The number of 5-card poker hands from a standard deck of 52 cards is The number of 47-card poker hands from a standard deck of cards is

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

View Full Document
Corollary 2 Algebraic manipulation Combinatorial proof : Counting arguments are used to show that both sides of an identity count the same objects in different ways.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 14

15_Counting - Permutations An ordered arrangement of r...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online