Contemporary Mathematics Topic 21 Miscellaneous Counting Methods Combining

Contemporary Mathematics Topic 21: Miscellaneous Counting Methods

Combining All the Counting Methods › In most situations, you do not know which counting method to use. › In these cases, you must deduce which method to use, or a combination of them. › The most important point to consider is that permutations require order to be important. Beyond that, there’s not a hard-and-fast rule and judgement must be employed.

Example 1: › If you have 5 workers, how many ways can 2 of them be selected in each of the following scenarios? A) One is assigned leader, one is assigned helper. B) They just do the job. › A TV network has 6 different half-hour programs during prime time (7 to 10 PM). You want to watch 3 programs one evening. How many choices do you have? If exactly 1 of the programs must be after 9 PM, how many choices do you have?

Permutations of Non-distinct Objects ›

Example 2: › How many ways can the letters in KANSAS be arranged? › How many ways can the letters in ALABAMA be arranged? › How many ways can the letters in MISSISSIPPI be arranged?

Example 3: › An advertiser has a contract for 20 weeks that provides 3 different ads each week. If it is decided than in no 2 weeks will the same 3 ads be shown, how many different ads are necessary? › A cable television network wishes to show 5 movies every day for 3 weeks (21 days) without having to show the same 5 movies any 2 days. What is the least number of movies needed? › What if the cable network wanted to do it for 8 weeks?