Can Ayush survive?

Probability Level 3

Ayush is trying to go to the coordinates ( 6 , 6 ) (6,6) from ( 0 , 0 ) (0,0) . But in the way, on the coordinates ( 3 , 1 ) , ( 4 , 1 ) , ( 3 , 2 ) , ( 4 , 2 ) (3,1),(4,1),(3,2),(4,2) werewolf, vampire, ghost, zombie are there respectively. Ayush has to avoid all of them to survive. How many ways Ayush can survive and reach ( 6 , 6 ) (6,6) successfully?

Note: Ayush can move only right or up.


The answer is 469.

Prince Loomba by Prince Loomba , 21, India

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1 solution

Prince Loomba
Oct 11, 2016

Total ways to reach 6,6=12C6.

Subtract the ways passing through 3,1 (4×8C3),

then the ways passing through 3,2 but not throught 3,1 that is, passing through 2,2 (6×7C3) and

then the ways passing through 4,1 not through 3,1 that is passing through 4,0 (7C2).

The answer is 469.

Note: Here I have not considered 4,2 as the both ways of reaching it are already blocked.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

You can also just count the ways that pass through 3,2 (10x7C3) and the ways that pass through 4,1 (5x7C2) and add them together then you would have gotten all the wrong paths since any paths that goes through 3,1 must also go through either 3,2 or 4,1 and the same case goes for 4,2. It is the same idea as yours but with just one step shorter. -I really like the question btw.

Abdo Reda - 2 years, 11 months ago

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Thnx^^ and also thanks for the alternate solution

Prince Loomba - 2 years, 9 months ago

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