Answer:
20
Explanation:
Here Karen must choose 3 color from 6. As every rod have different color and size we can say that every rod is different in both size and color. As here we do not care about the order of the rods, this is, Red Orange and Yellow is the same as Yellow Red and Orange, as if we simply rotate the triangle we will arrive to every combination that implies changing the order of the colors, we can use combinations.
We will use combinations to choose 3 objects from a set of 6. The general formula of picking r objects from n is:
nCr = n! / r!(n-r)!
Here our n=6 and r=3, so:
6 C 3 = 6! / 3!(6-3)! = [6*5*4*3*2*1] / [ (3*2*1)*(3*2*1)]
6 C 3 = [(6*5*4)*(3*2*1)] / [(3*2*1)*(3*2*1)] = (6*5*4) / (3*2*1)
6 C 3 = 120/6 = 20
So, Karen can make 20 different triangles combining the 6 rods she has.