{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

LrTrChVIIISIICombinationsCnt

LrTrChVIIISIICombinationsCnt - Dr Raja Latif Math 131(043...

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

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

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

View Full Document
Dr. Raja Latif. Math 131 (043) Sec: 8.2. Pg:2 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 at a time is given 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

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

View Full Document
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
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!

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 / 24

LrTrChVIIISIICombinationsCnt - Dr Raja Latif Math 131(043...

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

View Full Document
Ask a homework question - tutors are online