Question

Mack the bug starts at $(0,0)$ at noon and each minute moves one unit right or one unit up. He is trying to get to the point $(5,7)$. However, at $(4,3)$ there is a spider that will eat him if he goes through that point. In how many ways can Mack reach $(5,7)$?

Answer 1

Step-by-step explanation:

Given Mack the bug starts at $(0,0)$ at noon and each minute moves one unit right or one unit up. He is trying to get to the point $(5,7)$. However, at $(4,3)$ there is a spider that will eat him if he goes through that point. In how many ways can Mack reach $(5,7)$?

• According to question the number of ways to get the point from (0,0) to (5,7) will be
• (7 + 5)! / 7! 5!
• = 12! / 7! 5!
• = 479001600 / 604800
• = 792 ways
• Now from (0,0) to (2,3) it will be
• (3 + 2)! / 3! 2!
• = 5! / 3! 2!
• = 120 / 12
• = 10 ways.

Now we need to subtract , so 792 – 10 will be 782 ways or routes.

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