LrTrChVIIISIICombinationsCnt - Dr. Raja Latif. Math 131...

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

View Full Document Right Arrow Icon
Dr. Raja Latif. Math 131 (043) Sec: 8.2. Pg:1 Chapter 8 : Introduction to Probability and Statistics 8 . 2 : Combinations and Other Counting Principles Combinations of n Objects: To derive a formula for determing the number of combinations of n objects taken r at a time, written C n , r or n r we observe that each of the C n . r combinations of r objects can be permuted in r ! ways Each combination can be permuted in r ! ways  r objects r objects .......... r objects C n , r objects 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Dr. Raja Latif. Math 131 (043) Sec: 8.2. Pg:2 2
Background image of page 2
Dr. Raja Latif. Math 131 (043) Sec: 8.2. Pg:3 Thus, by the multiplication principle, the product r ! C n , r gives the number of permutations of n objects taken r at a time; that is, r ! C n , r P n , r from which we find r ! C n , r P n , r r ! C n , r n ! r ! n r ! . Conclusion: The number of combinations of n distict objects taken r atat imeisg iven by C n , r n ! r ! n r ! . where r n . Permutations with Repeated Objects: The number of distiguidhable permutations of n objects such that n 1 are of one type, n 2 3
Background image of page 3

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

View Full DocumentRight Arrow Icon
Dr. Raja Latif. Math 131 (043) Sec: 8.2. Pg:4 are of a second type, . ..and n k are of a kth type, where n 1 n 2 ... n k n ,is n ! n 1 ! n 1 !... n k ! . Assignment to Cells: Suppose n district objects are assigned to k ordered cells with n i objects in cell i i 1,2,. .., k and the order in which the objects are assigned to cell i is of no concern. The number of all such assignment is n ! n 1 ! n 1 !... n k ! , where n 1 n 2 n k n . 4
Background image of page 4
Dr. Raja Latif. Math 131 (043) Sec: 8.2. Pg:5 400T8.2B9. COMMITTEE In how many ways can a four-member committee be formed from a group of 17 people? The number of ways of selecting 4 of 17 people so that order is not important is 17 C 4 17! 4! 17 4 ! 17!
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/17/2009 for the course MATH MATH131 taught by Professor Dr.rajalatif during the Spring '09 term at King Fahd University of Petroleum & Minerals.

Page1 / 24

LrTrChVIIISIICombinationsCnt - Dr. Raja Latif. Math 131...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online