Franklin the fly starts at the point $(0,0)$ in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After $10$ steps, how many different points could Franklin end up at?

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Answer:

80 different points.

Step-by-step explanation:

right, left, up, or down = 4 possibilities x 2 since there is a coordinate with 2 numbers so,

8 possibilities.

8 x 10 = 80 possibilities.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. After $10 steps, the number of different points that could Franklin ends up at 1048576.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given that Franklin can move in 4 direction after each step, therefore, the number of choices that Franklin have is,

Number of points = 4×4×4×4×4×4×4×4×4×4 = 4¹⁰ = 1048576

Hence, After $10 steps, the number of different points that could Franklin ends up at 1048576.

Learn more about Multiplication:

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