Consider the grid of points shown here. Suppose that, starting at the point labeled A, you can go one step up or one step to the right at each move.

# Consider the grid of points shown here. Suppose that, starting at the point labeled A, you can go one step up or one step to the right at each move.

J
240 points

Consider the grid of points shown here. Suppose that, starting at the point labeled A, you can go one step up or one step to the right at each move. This procedure is continued until the point labeled B is reached. How many different paths from A to B are possible?

Hint: Note that to reach B from A, you must take 4 steps to the right and 3 steps upward.

Consider the
jeffp

8.7k points

There are only two possibilities -- to move up or right. If we think of possible ways to move up or right we could move in the following way,

right-right-right-right-up-up-up

but this is similar to problems we where find the number of ways to arrange letters in a word. In this case we have 7 different moves where 4 rights and 3 ups and indistinguishable,

$$\frac{7!}{4!3!} = 35$$ different paths.

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