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In how many ways can a person reach from A(0, 0) to B(6, 6) if they can walk either in the east direction or in the north direction?

A. 252
B. 36
C. 12
D. 18

User Machine
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1 Answer

6 votes

Final answer:

To reach from point A to point B, the person can take either 6 steps east and 6 steps north. Using the combination formula, we find that there are 924 ways to reach point B from point A.

Step-by-step explanation:

To solve this problem, we can use the concept of combinations. Since the person can only walk east or north, they have to take a total of 6 steps east and 6 steps north to reach point B. The order in which they take these steps does not matter, so we can use the combination formula.

The number of ways to reach from A to B is given by C(12, 6), which is equal to 12!/(6!(12-6)!). Solving this expression, we get C(12, 6) = 924.

Therefore, there are 924 ways for the person to reach from A(0, 0) to B(6, 6) if they can walk either in the east direction or in the north direction.

User David Carlisle
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