Lattice Paths and Combinatorics

The video tutorial explains how to calculate the number of shortest lattice paths on a coordinate plane, starting from (1, 2) and ending at (10, 10). It covers the concept of combinations to determine the number of paths, evaluates paths passing through a specific point (4, 5), and calculates paths that avoid this point. The tutorial uses a scientific calculator to demonstrate these calculations, providing a comprehensive understanding of lattice paths in combinatorics.

What is the formula used to calculate the number of shortest lattice paths?

• n plus k

• n minus k

• n times k

• n choose k

How many total steps are needed to move from (1, 2) to (10, 10) using the shortest path?

• 17

• 16

• 18

• 15

If a path takes 9 steps to the right, how many steps does it take upwards to reach (10, 10) from (1, 2)?

• 6

• 7

• 8

• 9

What is the value of 17 choose 9?

• 24,310

• 23,410

• 25,310

• 22,310

How many steps are required to move from (1, 2) to (4, 5) using the shortest path?

• 6

• 7

• 5

• 8

What is the number of shortest lattice paths from (1, 2) to (4, 5)?

• 10

• 20

• 25

• 15

How many shortest lattice paths are there from (4, 5) to (10, 10)?

• 262

• 562

• 362

• 462

What is the total number of paths from (1, 2) to (10, 10) that pass through (4, 5)?

• 9,240

• 8,240

• 10,240

• 11,240

How do you calculate the number of paths that avoid a specific point?

• Subtract paths through the point

• Multiply paths through the point

• Divide paths through the point

• Add paths through the point

What is the number of paths from (1, 2) to (10, 10) that avoid (4, 5)?

• 16,070

• 17,070

• 15,070

• 14,070