tags

tags

*# # # #*

Certain types of probability calculations involve dividing the number of outcomes associated with an event by the total number of possible outcomes. For simple problems, it is easy to count the outcomes, but in more complex situations manual counting can become laborious or impossible.

Fortunately, there are formulas for determining the number of ways in which members of a set can be arranged. Such arrangements are referred to as **permutations** or **combinations**, depending on whether the order in which the members are arranged is a distinguishing factor.

The number of different orders in which members of a group can be arranged for a group of *r* members taken *r* at a time is:

(r)(r-1)(r-2)...(1)

This is more easily expressed as simply r!.

When the order is a distinguishing factor, a group of n members taken r at a time results in a number of permutations equal to the first r terms of the following multiplication:

(n)(n-1)(n-2)...

This can be expressed as:

_{n}P_{r} = n! / (n - r)!

In combinations, order is not a distinguishing factor:

_{n}C_{r} = _{n}P_{r} / (r!) = n! / (n - r)!r!

For the special case of possible pairs in a group of *n* members, assuming order in a pair is not important, then:

r = 2

and the number of possible pairs is:

n(n - 1) / 2.

**Example:**How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?

Solution: 4! / (2!)(2!) = 6, but the subset {2,4} is not to be counted, so the answer is 5.

Given n items taken r at a time, to find the number of combinations in which x particular items are not present, simply reduce n by x and solve as one would a normal combination problem.

**Combinations of Groups**

If Group A has x members, Group B has y members, and Group C has z members, there are (x)(y)(z) possible combinations assuming that one member from each of the three groups is used in each combination, and assuming that the order is not a distinguishing factor. In general, if more than one member is taken at a time from each group, the number of combinations is the product of nCr (or nPr if appropriate) associated with each particular group.

The End, what is next?

Note: the page content was squeezed for you with a focus on , by Paperfree Magazine Team, editor -

Go ahead and share it!

*check this out, Permutations and Combinations*Tweet

Want more content related to "" ? Subscribe PaperFree Magazine!

We will send an email from PaperFree Magazine with the top content on this subject: , .

- PUBLISH CONTENT
- Real Estate Investment Principles by Billionaire Bruce Flatt
- Real Estate Investing Basics: 2 Ways of Real Estate Investment
- Back to Basics: Understanding Real Estate
- 5 Best Ways to Invest in Real Estate For Starters
- 7 Ways On How To Make Money In Real Estate
- 6 Factors To Look For Before Investing in Real Estate
- Return on Investment (ROI) In Real Estate & Its Calculation
- How Much Money To Invest in Real Estate
- Real Estate Business: 7 Challenges You Need To Know Before You Start
- Real Estate Investment Trust (REIT)
- Introduction of Real Estate Investment Trusts (REITs)
- Direct Real Estate Investment Vs REITs - Which One To Choose?
- REITS, Real Estate Funds & Real Estate Mutual Funds: The Comparison
- Equity Vs Mortgage Real Estate Investment Trust
- Assessing A Real Estate Investment Trust (FFO and AFFO)
- Real Estate Investment Trust (REIT) and Its Risks
- Counties by population based on United States Census
- Trump's tax report and tax avoidance leveraging Real Estate business
- Demographic trends are reshaping the real estate market in the US