A tortoise lives in a garden on a 7 × 5 plot of land as shown in the figure: в The tortoise is trying to get from point A(0,0) to point B(7,5) by walking along the edges of the grid in the garden, but only taking unit steps to the right or upwards. There is a small lake in the middle of the garden. (a) How many different paths can the tortoise follow from A to B that avoids the small lake in the middle of the garden? (Note: The tortoise can walk around the edges of the lake but can't swim across.)

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A tortoise lives in a garden on a 7 × 5 plot of land as shown in the figure:
в
The tortoise is trying to get from point A(0,0) to point B(7, 5) by walking along the edges of the grid
in the garden, but only taking unit steps to the right or upwards. There is a small lake in the middle
of the garden.
(a) How many different paths can the tortoise follow from A to B that avoids the small lake in the
middle of the garden?
(Note: The tortoise can walk around the edges of the lake but can't swim across.)
(b) The garden is renovated and the lake is expanded, with a new bridge going over the water to the
other side, connecting points (3, 1) and (3, 3). How many different paths can the tortoise follow
from A to B in this renovated garden?
в
A.
Transcribed Image Text:A tortoise lives in a garden on a 7 × 5 plot of land as shown in the figure: в The tortoise is trying to get from point A(0,0) to point B(7, 5) by walking along the edges of the grid in the garden, but only taking unit steps to the right or upwards. There is a small lake in the middle of the garden. (a) How many different paths can the tortoise follow from A to B that avoids the small lake in the middle of the garden? (Note: The tortoise can walk around the edges of the lake but can't swim across.) (b) The garden is renovated and the lake is expanded, with a new bridge going over the water to the other side, connecting points (3, 1) and (3, 3). How many different paths can the tortoise follow from A to B in this renovated garden? в A.
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