Other
MATH1302 Discussion Assignmment Unit 2 (Combinatronics)
- Course
- Institution
- Book
Peer assessment and discussion forum assignment for Discrete Mathematics.
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
More summaries for
-
COS1501 Assignment 3 2023
-
lagrange's theorem
-
Summary Discrete Mathematics, ISBN: 9781792901690 Discrete Structures in Mathematics (MATH265)
Seller
Follow
brianwanyonyi
Content preview
MATH 1302 Discrete Mathematics.Discussion Assignment Unit 2.
1. Explain in words why the equation (nk)=(n−k
n
) is true.
Solution.
The statement (nk)refers to combinations and is called “n choose k”. This means, out of a
total of n objects there are number of groups that can be defined of k quantity. For
instance, out of total eight (8) letters in the name WANYONYI, how many 2 letter
words, e.g., NO, WN, etc. meaningful or meaningless can be made, or 8 chooses 2,
written as (82).
With ()
n
k
combinations there are no repetitions and order does not matter. Therefore, let
us consider an example: ( )
50
4
50! = 50*49*48*47*…….
50! = 50*49*48!
This tells us that 48! Is part of the 50! hence implicitly in in the numerator of the
combination formula and cancels out the k! in the denominator part of the formula.
2. Use the definition (nk ) = k ! ( n−k
n!
)!
to show that the equation in question 1 is true.
Solution.
Substitute k with (n-k):
(n−k
n =
) ( n−k ) ! ( n−
n!
( n−k ) ) !
(n−k
n =
) ( n−k ) ! (nn−n+k
!
)!
(n−k
n =
) ( n−kn!) ! ( k ) !
Rearranging the equation gives us:
1|Brian Wanyonyi – University of the People.
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 brianwanyonyi. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
79373 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now