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Probability Level 5

Jeet planned his day of JEE well. On the day of the exam, he woke up early and decided to reach the exam hall as early as possible to attain peace of mind and soul in the exam hall. The path from his house to exam hall is a like a grid. Each black line represents one step he could take.

His house is at position A and the exam hall is at position B.In how many ways can he reach the exam hall if he has to take the shortest path and he is not allowed to pass through point M.

This is part of my set : Fun is a Student's Right

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The answer is 1916647.

Aniket Sanghi by Aniket Sanghi , 21, India

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2 solutions

Aniket Sanghi
Apr 14, 2016

14C6 (12C6 - 6C3* 6C3) + 1 + 13C5 ( 11C6 - 5C2 * 6C3) + 10C6 * 8C2 = 1916647 \boxed{1916647}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Could you explain the solution please?

Upamanyu Mukharji - 3 years, 11 months ago

GREAT PROBLEM !

Ankit Kumar Jain - 3 years, 2 months ago

I have a doubt. In the expression 13C5(11C6-5C2*6C3), isn't a multiple of 2 missing as there are 2 paths that lead from the first zone(8x6 grid) to the next zone (6x6 grid) ( one which is outside and clearly visible and the other which lies along the boundary of the two zones).Or is that a case of double counting? Help is appreciated.

Jacob Sony - 1 year, 11 months ago
Mayank Singh
Apr 6, 2016

Great work

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks!

And......Best of luck for your JEE ADVANCED

Aniket Sanghi - 5 years, 2 months ago

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Welcome !!!!!!!!!!!!!!!!!!!!

Mayank Singh - 5 years, 2 months ago

Can u provide the solution?

Aditya Kumar - 5 years, 2 months ago

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Do you know the basics to solve such questions?

Aniket Sanghi - 5 years, 2 months ago

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Yes. First of all your question was a little confusing. You need to mention that "path followed must pertain to this diagram itself." I considered the empty spaces as incomplete figure and took squares in them. And yes it would be nice of you if you provided the solution as I got a different answer.

Aditya Kumar - 5 years, 2 months ago

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@Aditya Kumar – The ques is based on the diagram only , there is no point to argue in it.

Aniket Sanghi - 5 years, 2 months ago

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