Question

The local theater located six blocks east and four blocks south of the school is showing free movies on Friday after school. You cannot miss this opportunity to see free movies, but are only allowed to walk east or south from the school. How many different paths lead from the school to the theater?

a) 10 different paths
b) 15 different paths
c) 20 different paths
d) 210 different paths

Answer 1

To find the number of different paths from the school to the theater, you can use the concept of permutations. In this case, the number of different paths is 210.

Step-by-step explanation:

The student needs to find the number of different paths that lead from the school to the theater.

Since the student can only walk east or south, they can create a grid to represent their movement. Each block east and each block south will be represented by a step in the grid.

In this case, the student needs to walk 6 blocks east and 4 blocks south. To find the number of different paths, they can use the concept of permutations. The formula for permutations is nCr, where n represents the total number of steps and r represents the number of east or south steps.

In this case, n = 6 + 4 = 10 and r = 6, since the student needs to take 6 east steps. Plugging these values into the permutation formula, the number of different paths is 10C6 = 210.

Therefore, the correct answer is d) 210 different paths.