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Unformatted text preview: Probability for Engineering Applications Assignment #3, due at the beginning of class on Thursday, February 9 th , 2006 1. (2 pts) (Textbook exercise 2.47) In this problem we derive the multinomial coeffi- cient. Suppose we partition a set of n distinct objects into m subsets B 1 , B 2 , , B m of size k 1 , k 2 , , k m , respectively, where k i i and k 1 + k 2 + + k m = n . a. Let N i denote the number of possible outcomes when the i th subset is selected. Show that N 1 = n k 1 ! , N 2 = n- k 1 k 2 ! , , N m- 1 = n- k 1- - k m- 2 k m- 1 ! , N m = 1 Basically we are interested in the following: We have a total on n objects. From these, we first pick k 1 objects. How many ways of doing this (denote this by N 1 )? From the remaining objects, we now pick k 2 objects. How many ways of doing this (denote this by N 2 )? And so on. b. Show that the total number of partitions is then N 1 N 2 N m = n !...
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This note was uploaded on 09/07/2009 for the course ECE 302 taught by Professor Gelfand during the Fall '08 term at Purdue University-West Lafayette.
- Fall '08