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A rectangular city is divided by streets into squares. There are n such squares from north to south and k squares from east to west. Find the number of shortest walks from the north-eastern end of the city to the south-western end.

A rectangular city is divided by streets into squares. There are n such squares from north to south and k squares from east to west. Find the number of shortest walks from the north-eastern end of the city to the south-western end.

Grade:10

3 Answers

Arun
25763 Points
one year ago
Dear student
 
As there are n squares from North to south
And k squsres from East to west.
Hence there are n+1 and k+1 lines respectively.
 
 
Hence total required ways = (n+k+2)! /( n+1)! (k+1)!
Sayantan Garai
117 Points
one year ago
But the answer given is (n+k) Ck.
 
 
 
...................??..??....?.???!! /?.................).. C...... 
Arun
25763 Points
one year ago
Oh sorry
 
We count from 0.
Hence (n+k)!/ n! k!
Or we can also say n+kCk or n+kCn.
 
Hope now you understand

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