Carlota has several strips of trim she wishes to use as a triangluar border for a section of a decorative quilt she is going to make. The strips measure 3 cm, 4 cm, 5 cm, 6 cm, and 12 cm.
How many different triangles could Carlota make with the strips?

Question

Vocaloid · Answer

Using the combination formula there are 5C3 ways to pick three pieces out of 5

However, that cannot be the final answer, as not every three sides can make a triangle. In order  for three sides to make a triangle, each pair of two sides must add up to greater than the third. So determine how many combinations *can’t* make a triangle and subtract that from 5C3