Triangular grid in cartesian plane!

Find the number of ways to from (0,0) to (8,8) in the right angled isosceles triangle forming the sides:

1) (0,0) to (8,0)

2) (8,0) to (8,8)

3) (0,0) to (8,8)

You can only go in positive vertical or horizontal directions(only integer co-ordinates). Diagonals are not allowed.

Bonus: Try to find the number of ways for a general case like (0,0) to (m,m)

#Combinatorics #Numberofways #Triangulargrid

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

Try this problem @Surya Prakash @Satyajit Mohanty @Nihar Mahajan @Swapnil Das

Saarthak Marathe - 5 years, 6 months ago

Can we go up and sideways only from the integral values or from anywhere in between?

Bhavya Sheth - 5 years, 6 months ago

Only integral values

Saarthak Marathe - 5 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$