Interview
Fundamental Counting Principle
- Course
- Institution
An explanation of the Fundamental Counting Principle.
[Show more]
Seller
Follow
kalebroodt
Content preview
Fundamental counting principal (incorporating factorials):Now that we are able to employ factorials to condense our calculations for the fundamental
counting principle, we can progress to more challenging examples.
Example:
A grade 12 learner has Accounting, Science, Xhosa and Mathematics textbooks on their bookshelf
and wants to rearrange them. How many different ways can the books be arranged?
4 books and 4 spaces, the number of arrangements is 4! = 4 × 3 × 2 × 1 = 24
Example:
In how many different ways can the letters of the word MARKS be arranged? Assume
that repetition of letters is not permitted.
Number of letters: 5
∴ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑟𝑟𝑎𝑛𝑔𝑒𝑚𝑒𝑛𝑡𝑠 = 5! = 5 × 4 × 3 × 2 × 1 = 120.
Example:
4 different History books, 5 different Geography books and 2 different Science books are placed on
a book shelf.
a) how many different ways can they be arranged?
b) how many different ways can they be arranged if books of the same subject must be
placed together?
a) Total number of books is 11,
∴ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑎𝑟𝑟𝑎𝑛𝑔𝑒𝑚𝑒𝑛𝑡𝑠 = 11! = 39916800.
b) in order to solve this problem, we can treat each subject as occupying one space:
History Geography Science
Four books, number of Five books, number of Two books, number of
arrangements 𝟒! arrangements 𝟓! arrangements 𝟐!
But since there are 3 subjects there are 3! Ways in which each of the subjects can be
arranged
∴ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑟𝑟𝑎𝑛𝑔𝑒𝑚𝑒𝑛𝑡𝑠 = 3! × [4! × 5! × 2!] = 34560.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller kalebroodt. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.91. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
73314 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now