Going to the Castle - Part 3

Probability Level 1

I was on vacation in England, and wanted to visit the Tower of London. The roads were laid out on a grid map, and and the castle was 4 blocks north and 5 blocks east. I also wanted to visit the Apple store along the way, and check out the new IWatch.

If I were to travel only north and east, how many routes did I have to get to the castle?

See Part 1 , Part 2 , Part 4 , and Part 5 .

{ 4 \choose 2} \times { 4 \choose 1 }

{ 4 \choose 2 } \times { 4 \choose 2 }

{ 5 \choose 2 } \times { 5 \choose 2 }

{ 5 \choose 2 } \times { 4 \choose 2 }

2 solutions

Rohit Sachdeva
May 9, 2015

To reach the tower we have to first go to A, then take path AB, then go to tower from B

The point A is at (2N,2E). The total number of ways to reach point A is arrangement of 2N's & 2E's which can be done in $^{4}C_{2}$ ways.

The tower is at (2N,2E) from point B. The total number of ways to reach the tower from point B is arrangement of 2N's & 2E's which can be done in $^{4}C_{2}$ ways

So ways to reach the tower going through apple store(AB) is $^{4}C_{2} * ^{4}C_{2}$

Nicely done!

Chung Kevin - 6 years ago

If the store is on the right side, you get (5:2) and if it’s on the left side,we get (4:2), and if it’s on the right side, we get (4:2) ways to get to the castle and if the store is on the left side, we get (5:2) ways to get to the castle, thus, using communitive property of multiplication, we get (5:2) * (4:2)

NOTE: (a:b) = aCb = a choose b = (a!)/((a-b)!b!)

Saksham Hassanandani - 2 years, 3 months ago

Brody Burkett
May 30, 2018

There are 6 ways to reach the Apple Store provided you go only north and east. There are also only 6 ways to reach the tower from the Apple Store given the same rules. Hence 6 (6) = 36.

Going to the Castle - Part 3

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