So how do we go about them?..Let's unlock that door of mystery today.
Look at the first of the above set of images : A square.
Now if you position yourself in 8 of those spots, and imagine how your left,right and relative surroundings will look like, you should be able to realize that there are only 2 distinct orientations as denoted by distinct colors in the image. So we can place the first object in these 2 distinct orientations and simply arrange the remaining objects. Hence we get total arrangements as : 2*7! for the square.
Similarly if you now look at the other two images in the set, you should be able to achieve the following results :
Equilateral triangle : 3*8! and Rectangle : 5*9! by following the same logic.
Phase 1 of your learning is complete !
Let's proceed to phase 2 now : Extending the learning and gaining more perspective.
Now here if you look to place yourself in the 8 possible spots you realize that they all are distinct orientations due to asymmetry of 2-same and 1-different side. Hence, the answer here will be : 8*7!
If you are with me till now, you should be able to reach the generalization found in several sources for a circular arrangement : 1*(n - 1)! or simply (n - 1)!.
Phase 2 complete !
Last and final phase of this topic comes down to a practice question which you should try and find the answer to. To confirm the answer look into comments but only when you have figured it out yourself. Else, I would advise you to go through the article again and find your way back here when you are ready.
Cheers!
AS
I hope everyone reaches this point with comfort and find their answer to be : 9*8!
ReplyDeleteThanks for your time. Many more such articles to come. Keep following !
GooD Job !
ReplyDeleteThanks for the feedback..Keep following for more :)
Delete