l05_usrepl

# l05_usrepl - Sampling III Unordered Sampling with...

This preview shows pages 1–6. Sign up to view the full content.

02/02/2009 CS206 - Intro. to Discrete Structures II 1 Sampling III: Unordered Sampling with Replacement Reading: Ross, Ch 1., Sec. 5. Rosen, Ch 5., Sec. 5. Monday, February 2, 2009

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

View Full Document
02/02/2009 CS206 - Intro. to Discrete Structures II 2 Example 1 • How many ways to pick four pieces of fruit from a bowl of apples, oranges, and pears? Order does not matter, only the type of fruit. (There enough pieces to pick four of each type.) Do we need to know how many pieces of fruit in the bowl? Say 50. Is the answer C(50,4)? No! Because not all 50 are different. Monday, February 2, 2009
02/02/2009 CS206 - Intro. to Discrete Structures II 3 Example 1 (cont’d) • Consider this: There are three bins, one each for A, O, and P. Need to distribute four (generic) pieces of fruit into the three bins. Fruit (generic) A O P A O P A O P Monday, February 2, 2009

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

View Full Document
02/02/2009 CS206 - Intro. to Discrete Structures II 4 Example 1 (cont’d) • Or consider this… Place two bars between four pieces of fruit. (4+2)! / [ 4! ¢ 2! ] = 6! / [ 4! ¢ 2! ] = 15 = C(6,4) - pick 4 pieces from a set of 4+3-1 A O P , Monday, February 2, 2009
CS206 - Intro. to Discrete Structures II 5 Combinations with Repetition • Given a set of r types of elements, there are C(n+r-1,r-1) ways to choose n elements, with repetition. E.g., Fruit example: r = 3 types of fruit. Ways of picking n = 4 pieces:

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 21

l05_usrepl - Sampling III Unordered Sampling with...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online