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Permutations and Combinations | Counting | Don't Memorise - YouTube
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The formula for N C R is 'N factorial, divided by R'
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factorial times 'N minus R' factorial.
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What is this? This is the formula for combinations,
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but it is not the best way to understand it !
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And what is NPR. It's N factorial over 'N minus R' factorial.
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And this again, is not the best way to understand permutations!
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In many books, and videos you would be asked to use this formula,
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if we have to select our things out of N.
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And we would be asked to use this formula if
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we have to arrange our things out of n.
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I can assure you that if you understand just these two formulae,
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you will never really understand permutations and combinations.
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There's only one thing you should understand well
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if you wish to master this topic!
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And that's counting !
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If you're able to count well,
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then the topic of permutations and combinations will be a walk in the park!
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Of course, the counting will not be as simple as counting on your fingers.
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It's a little more advanced. But don't worry. Counting is easy!
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Let's say we have three pens, and two markers.
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Every item is distinct. No two items are the same.
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Here's your first question based on counting.
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In how many ways can we pick any one items from these five?
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Understand the question well.
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In how many ways, can we pick any one item from three pens and two markers?
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In how many ways do you think we can do this?
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Look at it logically.
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We can either pick the first pen.
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We can call it P1 or the second pen or maybe the third pen.
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Or maybe we pick a marker.
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The first one or the second one!
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We kept saying OR.
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This or this or this and so on.
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You can see that there are five ways in which we can pick any one item.
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And how do we get a five?
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Three ways in which a pen can be picked.
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Plus two ways in which your marker can be picked .Five ways in all.
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This is the first rule of counting .
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Or !
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Or, always means addition.
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First Pen or the second pen or the third.
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Three ways in which a pen can be picked.
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And similarly, two ways in which your marker can be picked.
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Or always means addition.
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Now let me ask you another one.
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In how many ways can we pick one pen and one marker?
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one Pen and one marker!
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Tell me what you think?
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We have to pick a pen and a marker.
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In how many ways can we pick a pen?
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We pick either the first or the second or the third?
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Now having picked one pen we need to pick a marker.
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Maybe after picking the first pen, we pick the first marker.
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Or May be after picking the first pen, we pick the second marker.
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So one way is p 1 m 1, and another is p 1 m 2.
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Or Maybe we pick p 2 and then m 1 or p 2 and m 2 .
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In all we can see that there are six ways in which we can pick a pen and a marker.
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Which are the six ways?
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p 1 m 1,
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p 1 m 2,
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p 2 m 1, p 2 m 2, p 3 m 1 and p 3 m 2 .
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And how did we get a 6?
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3 ways times two ways.
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Multiplication!
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'And' is another rule of counting, it always means multiplication.
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One pen and one marker 'three ways' multiplied by 'two ways'.
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One pen or one marker three ways plus two ways.
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If you understand these two rules of counting, trust me!
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You will be able to solve most problems based on permutations and combinations!
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And this is nothing new!
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I am sure you have used this many times in life.
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Look at this picture!
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How many circles do you see?
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I doubt you counted each circle.
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Instead of counting each circle,
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you would have noticed that there are six columns and four rows.
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Because it's AND the number of Circles will be 6 x 4.
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24 and all.
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Don't forget the two basic Rules.
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AND is multiplication OR is addition.
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The topic of permutations
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and combinations is not liked by many students and maybe you as well.
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So we have covered as many topics and examples as we can.
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And I can assure you that if you watch all our videos based on this topic,
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you will master the concepts!
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So take some time, go through our sessions,
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and you will realize how simple this topic is!
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