in Combinatory recategorized by
564 views
7 votes
7 votes

Consider a $3 \times 11$ rectangular grid as depicted in Figure $1,$ formed by $33$ tiles of area $1\text{m}^2.$ A staircase walk is a path in the grid which moves only right or up.


How many staircase walks are there from $\text{A}$ to $\text{B}$ which start by going to the right two times?

in Combinatory recategorized by
564 views

1 comment

0
0

2 Answers

8 votes
8 votes
Best answer

Answer is 220

we will see why

selected by
4 votes
4 votes

We can only reach the grid point $(2, 0)$ by making two moves to the right in the beginning. Therefore the total number of staircase walks on this grid that start by moving right twice is exactly the same as the number of staircase walks from $(2, 0)$ to $\text{B}$ namely $^{12}\text{C}_{3}.$ In other words we need to choose $3$ up moves out of a total of $12$ remaining moves to make it to $\text{B}$ (the rest are right moves).

Video Solution:

https://youtu.be/tqjuxfutFHg?t=2917

edited by
Answer:

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true