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<html><table height="500" width="1000" border="2"><TR height="5" width="1000"><strong><center><marquee><font color="Green"><h1>APTITUDE</h1></center></strong></font></TR></marquee><TR><TD align="left" width="200" valign="top"><table><TR><a href="numbers.html"><strong>Numbers</strong></a></TR><br><TR><a href="hcf.html"><strong>H.C.F and L.C.M</strong></a></TR><br><TR><a href="dec.html" target="right"><strong>Decimal Fractions</strong></a></TR><br><TR><a href="simplification.html"><strong>Simplification</strong></a></TR><br><TR><a href="squareandcuberoot.html" target="right"><strong>Square and Cube roots</strong></a></TR><br><TR><a href="average.html" ><strong>Average</strong></a></TR><br><TR><a href="pnumbers.html" ><strong>Problems on Numbers</strong></a></TR><br><TR><a href="problemsonages.html"><strong>Problems on Ages</strong></a></TR><br><TR><a href="surdsandindices.html"><strong>Surds and Indices</strong></a></TR><br><TR><a href="percent.html" target="right"><strong>Percentage</strong></a></TR><br><TR><a href="profitandloss.html" target="right"><strong>Profit and Loss</strong></a></TR><br><TR><a href="ratioandproportion.html" target="right"><strong>Ratio And Proportions</strong></a></TR><br><TR><a href="partnership.html"><strong>Partnership</strong></a></TR><br><TR><a href="chainrule1.html"><strong>Chain Rule</strong></a></TR><br><TR><a href="timeandwork.html" target="right"><strong>Time and Work</strong></a></TR><br><TR><a href="pipesandcisterns.html" target="right"><strong>Pipes and Cisterns</strong></a></TR><br><TR><a href="timeanddistance.html"><strong>Time and Distance</strong></a></TR><br><TR><a href="trains.html" target="right"><strong>Trains</strong></a></TR><br><TR><a href="boats.html"><strong>Boats and Streams</strong></a></TR><br><TR><a href="alligation.html"><strong>Alligation or Mixture </strong></a></TR><br><TR><a href="simple.html" target="right"><strong>Simple Interest</strong></a></TR><br><TR><a href="CI.html" target="right"><strong>Compound Interest</strong></a></TR><br><TR><a href=""><strong>Logorithms</strong></a></TR><br><TR><a href="areas.html" target="right"><strong>Areas</strong></a></TR><br><TR><a href="volume.html" target="right"><strong>Volume and Surface area</strong></a></TR><br><TR><a href="races.html" target="right"><strong>Races and Games of Skill</strong></a></TR><br><TR><a href="calendar.html" target="right"><strong>Calendar</strong></a></TR><br><TR><a href="clocks.html" target="right"><strong>Clocks</strong></a></TR><br><TR><a href="" target="right"><strong>Stocks ans Shares</strong></a></TR><br><TR><a href="true.html" target="right"><strong>True Discount</strong></a></TR><br><TR><a href="banker1.html" target="right"><strong>Bankers Discount</strong></a></TR><br><TR><a href="oddseries.html" target="right"><strong>Oddmanout and Series</strong></a></TR><br><TR><a href=""><strong>Data Interpretation</strong></a></TR><br><TR><a href="probability.html"><strong>probability</strong></a></TR><br><TR><a href="percom1.html" target="right" ><strong>Permutations and Combinations</strong></a></TR><br><TR><a href="pinkivijji_puzzles.html" target="right"><strong>Puzzles</strong></a></TR></table></TD><TD valign="top"><a href="percom1.html" target="right"><strong>BACK</strong></a><br><br><font size="5"><center><b><u>CONCEPT</u></b></center></font><font size="4"><pre> <strong>Formulae<strong></strong>:-<br><br>-> Factorial Notation :- Let n be positive integer.Then ,factorial n dentoed by n! is defined as n! = n(n-1)(n-2). . . . . . . .3.2.1 eg:- 5! = (5 * 4* 3 * 2 * 1) = 120 0! = 1<br>->Permutations :- The different arrangements of a given number of things by taking some or all at a time,are called permutations. eg:- All permutations( or arrangements)made with the letters a,b,c by taking two at a time are (ab,ba,ac,ca,bc,cb)<br>->Numbers of permutations :- Number of all permutations of n things , taken r at a time is given by nPr = n(n-1)(n-2). . .. . . (n-r+1) = n! / (n-r)!<br>->An Important Result :- If there are n objects of which p1 are alike of one kind ; p2 are alike of another kind ; p3 are alike of third kind and so on and pr are alike of rth kind, such that (p1+p2+. . . . . . . . pr) = nThen,number of permutations of these n objects is: n! / (p1!).(p2!). . . . .(pr!)<br><br>->Combinations :- Each of different groups or selections which can be formed by taking some or all of a number of objects,is called a combination. eg:- Suppose we want to select two out of three boys A,B,C . then ,possible selection are AB,BC & CA. Note that AB and BA represent the same selection.-> Number of Combination :- The number of all combination of n things taken r at atime is: nCr = n! / (r!)(n-r)! = n(n-1)(n-2). . . . . . . tor factors / r!<br>Note that : nCn = 1 and nC0 =1An Important Result : nCr = nC(n-r)<font size="3"><a href="percom1.html" target="right"><strong>BACK</strong></a></font></pre></font></TD></TR></table></html>⌨️ 快捷键说明
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