Choose,Notation,choose,notatio education N Choose R Notation
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"n choose r" notation is widely used in combinatorics, the studyof the number of ways of doing something there is, and also has a closeconnection with Pascal's triangle. In this article, however, I focus onexplaining the various ways n choose r can be written, and how to interpret andunderstand this notation.Before I even attempt to explain how to interpret "n choose r"notation, it's worth mentioning that mathematicians have many ways of writingit in equations:1. nCrNote that this version has a few different subversions. You can have:i) n as a superscript and r as a subscript. Or even...ii) Both of n and r as subscripts.2. nr (this version is usually written with a pair of long brackets around the nand r.3. C(n,r)Really, it's all a matter of taste - you may have thought that opinionsdidn't come into the equation with mathematics, but actually mathematiciansquite enjoy this sort of thing - Some stick adamantly to one notation,convinced that what they are using is "official", and spend theirfree time trying to convert other mathematicians to their ways, andparticipating in heated debates, others enjoy switching between many differentways depending on what takes their fancy or what mood they're in, others mayeven have a different notation for each day of the week! So, it's up to you. Toavoid offending anyone, however, I'll just steer clear of this controversialtopic and just write n choose r in words each time.Basically, n choose r just means the number of ways of choosing r objectsfrom n distinct objects. So if I have four sweets, coloured red, yellow, greenand blue, and you could choose any two of them, that would be 4 choose 2. Butwhat does 4 choose 2 actually equal? We can list the different choices youcould make (called combinations) below:R and YR and GR and BY and GY and BG and BThis gives a total of 6 different choices you could make. Notice that orderdoes not matter. So if you picked the red then the yellow sweet, then we arecounting this the same as if you picked the yellow then the red sweet.Below are a few examples which you can check yourself:· 4 choose 1 is 4· 4 choose 4 is 1· 4 choose 0 is 1· 5 choose 3 is 10· 6 choose 3 is 20After trying it out a few times by listing the combinations, you shouldbegin to feel more comfortable at using n choose r notation. However, once youhave understood how to do this, there is much more fun to be had. Did you knowthat you can save yourself time by using the formula n!/(r!(n-r)!), which alsohappens to be the formula for Pascal's triangle? Enjoy finding out more aboutthis topic in the links below! Normal 0 false false false EN-GB X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable{mso-style-name:"Table Normal";mso-tstyle-rowband-size:0;mso-tstyle-colband-size:0;mso-style-noshow:yes;mso-style-priority:99;mso-style-qformat:yes;mso-style-parent:"";mso-padding-alt:0cm 5.4pt 0cm 5.4pt;mso-para-margin-top:0cm;mso-para-margin-right:0cm;mso-para-margin-bottom:10.0pt;mso-para-margin-left:0cm;line-height:115%;mso-pagination:widow-orphan;font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;}
Choose,Notation,choose,notatio