If you have sticks of length 1, 2, 3, 4, 5, 6, 7, 8 and 9 cm. How many different triangles con you make using 3 sticks?

Question

If you have sticks which measure 1, 2, 3, 4, 5, 6, 7, 8 and 9 cm (one of each). How many different triangles can you make using three of the sticks?

Answer 1

answer:
34 is the answer

Comments

Please explain the answer

Answer 2

Yes there are two formulas.
One is for when there are an even numbers of sticks and
the other is for when there are an odd number of sticks.

If you have sticks of lengths 1,2,3,...,n inches

The formula for when n is even is n(n-2)(2n-5)/24

The formula for when n is odd is (n-1)(n-3)(2n-1)/24

The case above is when there are 9 sticks. Since 9 is odd,
we use the formula, (n-1)(n-3)(2n-1)/24
(n-1)(n-3)(2n-1)/24 = (9-1)*(9-3)*((2*9)-1) /24
=(8*6*17)/24
=34