Question

In how many ways a rook can go from SouthEast to northwest corner of 8×8 chess board if travels only upwards or left?

Comments

is it 14 ?

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No sir. Options given are :

(A) 14P7
(B) 14C7
(C) 2^7
(D) 14!

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To reach north west corner, we need to move 7 times left and 7 times up.  

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Thank you sir.

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But it is not yet solved .

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Sorry I have made the mistake in calculation: its 3432 which is 14C7

https://www.khanacademy.org/math/math-for-fun-and-glory/puzzles/brain-teasers/v/path-counting-brain-teaser

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Here, question is slightly more trickier as root can jump multiple squares :)

Answer 1

This is an example of Permutation with repeated characters. 

To go to from (0,0) (consider, southeast corner) to (8,8) (consider northwest corner) we need to take 7 Up turn and 7 right turn. It means that its a forming a string like UUUUUUURRRRRRR (Whatever the way you go, you have to take 7 Up and 7 right to reach (8,8)). Now our job is it find the how many permutation can be formed from this string. Which is a very simple task. 

Total Number of permutation will be : ( factorial(14) / (factorial(7) * factorial(7))). Which is equivalent to 14C7.

Hence option B is correct. 

Comments

yes. The question setter would have meant this. But the other can be a programming question. Like Google and all ask such questions.

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Sir, Then please mark it as best answer :P :P

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ok :)