Strange city

Probability Level 3

The streets of a city are in square grids. There are seven streets running north and south, and six streets running along east-west. Find the number of ways in which a person can travel from the north-west corner to the south-east corner through the shortest possible distance.

462 926 625 248

Arkodipto Dutta by Arkodipto Dutta , 19, India

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2 solutions

Arkodipto Dutta
Jun 10, 2016

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Did you notice that ( 11 5 ) = 462 \dbinom{11}5 = 462 ? Coincidence?

Pi Han Goh - 5 years ago
Chew-Seong Cheong
Jun 12, 2016

The number of ways of going from a corner of to another in a square grid of m × n m \times n paths (streets) is given by ( reference ):

N = ( m + n − 2 min ⁡ ( m , n ) − 1 ) N = { m+n-2 \choose \min (m,n) - 1 }

For 7 × 6 7 \times 6 paths, we have N = ( 7 + 6 − 2 6 − 1 ) = ( 11 5 ) = 462 \displaystyle N = { 7+6-2 \choose 6 - 1 } = { 11 \choose 5 } = \boxed{462}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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