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![[Post New]](/templates/default/images/icon_minipost_new.gif) 24 Mar 2008 22:03:41 IST
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If 3 squares are selected at random from a chessboard,
then the probability that they form the letter L is :
a.)196 / 64 C 3 b.) 49 / 64 C 3
c.)36 / 64 C 3 d.) 98 / 64 C 3
This is a good one i think!
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24 Mar 2008 22:08:21 IST
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edited:
will post in a couple of sec
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24 Mar 2008 22:09:22 IST
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Just count all the L shapes possible...
now in a 2x2 square there are 4 L shapes
so to count all 2x2 squares
consider row of 8 squares
so to choose 2 consecutive squares, 7 ways
similarly vertically 7 ways
so 7*7=49 total 2x2 boxes
so
49*4=196 total Ls
so P=196/64C3
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24 Mar 2008 22:10:13 IST
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yeah a) only
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24 Mar 2008 22:11:04 IST
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but i edited initially cuz there can be bigger L formations also...
but then i saw max itself is 198 only
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24 Mar 2008 22:12:02 IST
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i think the qn implies only 3 squares with 2 common sides joined to form Ls
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24 Mar 2008 22:12:24 IST
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akhil wat do u say?
wat abt bigger L formations??
it comes down to wat u mean by an L actually
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24 Mar 2008 22:13:53 IST
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thts wat i thot initially
n got a...but edited cuz v can also have more na?
lik 5 sq etc ths also a symmetric L...
but well i was stupid...maximum itself is 198 only...
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24 Mar 2008 22:16:11 IST
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neway considerin L as a shape in which the 2 legs r equal in length how many r possible...
an extension of prev question
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24 Mar 2008 22:20:00 IST
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it should be quite easy...
just select one row,
select 2 in that, and in one of the columns select the next square
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24 Mar 2008 22:21:15 IST
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Ur answer would be
8C1*8C2*2C1*7/64C3
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24 Mar 2008 22:27:32 IST
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its quite direct lik u said
its st away 49*64
wid each sq as the joint of the L( i mean the turning pt) i can make 49 sq(as v have7*7)
64 such joints possible
so 64*49
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24 Mar 2008 22:29:03 IST
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Good work & nice discussion......u r correct Gokul I should have mentioned that.
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24 Mar 2008 22:29:04 IST
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akhil, wat say?
@ sushmi: thts quite easy too.. i mean all the Ls
refer akhil's post and my prev post
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24 Mar 2008 22:32:02 IST
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Yeah it was easy.....i found this quesn nearby and posted it  as u wanted more quesns.
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