5. Lattice paths with diagonal steps. A diagonal step in a lattice path moves 1 unit in the r-direction and 1-unit in the y direction. | (5, 5) (0,0) (a) For each k with 0

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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5. Lattice paths with diagonal steps. A diagonal step in a lattice path moves 1 unit in the
r-direction and 1-unit in the y direction.
|
(5,5)
(0,0)
(a) For each k with 0 < k < 5, determine the number of lattice paths with diagonal steps
from (0,0) to (5,5) that have exactly k diagonal steps. (A lattice path from (0, 0) to
(5, 5) with 1 diagonal step is displayed above.)
(b) Add your results from part (a) to determine the total number of lattice paths from (0,0)
to (5, 5) with diagonal steps.
(c) Using E notation, give a summation formula for the number of lattice paths with diagonal
steps from (0,0) to (n, n).
Transcribed Image Text:5. Lattice paths with diagonal steps. A diagonal step in a lattice path moves 1 unit in the r-direction and 1-unit in the y direction. | (5,5) (0,0) (a) For each k with 0 < k < 5, determine the number of lattice paths with diagonal steps from (0,0) to (5,5) that have exactly k diagonal steps. (A lattice path from (0, 0) to (5, 5) with 1 diagonal step is displayed above.) (b) Add your results from part (a) to determine the total number of lattice paths from (0,0) to (5, 5) with diagonal steps. (c) Using E notation, give a summation formula for the number of lattice paths with diagonal steps from (0,0) to (n, n).
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