1 / 2

Counting Permutations When Indistinguishable Objects May Exist

Counting Permutations When Indistinguishable Objects May Exist. How many rows , each one consisting of 3 A’s 1 B, and 4 C’s are there? (Here are some such rows: BACCCAAC ABCACACC CCCCAAAB Etc.) Answer: (3+1+4)! / (3!1!4!). In general:

verdad
Download Presentation

Counting Permutations When Indistinguishable Objects May Exist

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Counting Permutations When Indistinguishable Objects May Exist How many rows , each one consisting of 3 A’s 1 B, and 4 C’s are there? (Here are some such rows: BACCCAAC ABCACACC CCCCAAAB Etc.) Answer: (3+1+4)! / (3!1!4!).

  2. In general: k distinct types of objects are given, where k is a positive integer. Positive integers ni for i=1,…k are given. k is a given positive integer. How many rows are there, each one including ni objects of type i for i=1, …, k and no other objects? Answer: Let n=n1 + … +nk. Then the number of rows is n!/(n1! … nk!).

More Related