Lattice Paths and Combinatorics

Lattice Paths and Combinatorics

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Hard

CCSS
HSA.APR.C.5, HSF.IF.A.1, 8.F.A.1

Standards-aligned

Created by

Jackson Turner

FREE Resource

Standards-aligned

CCSS.HSA.APR.C.5
,
CCSS.HSF.IF.A.1
,
CCSS.8.F.A.1
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.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSA.APR.C.5

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

17

16

18

15

Tags

CCSS.HSF.IF.A.1

CCSS.8.F.A.1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSA.APR.C.5

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of 17 choose 9?

24,310

23,410

25,310

22,310

Tags

CCSS.HSA.APR.C.5

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

6

7

5

8

Tags

CCSS.HSA.APR.C.5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

10

20

25

15

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

262

562

362

462

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