A bag contains some sticks with lengths three feet, four feet, five feet, six feet, seven feet, and eight feet. Three sticks are chosen at random.
a) What is the probability that a triangle can be formed with the three chosen sticks?
b) What is the probability a right triangle can be formed with the three sticks?
+128399 C(6, 3) = 30 possibilities
3 4 5 6 7 8
Not all will work......we must satisfy the triangle inequality that says the sum of any two side lengths of a triangle must exceed the length of the remaining side
Possible lengths
3 - 4 - 5 3 - 5 - 6 3 - 6 - 7 3 - 7 - 8 4 - 5 - 6 4 - 6 - 7 4 - 7 - 8 5 - 6 - 7
3 - 4 - 6 3 - 5 - 7 3 - 6 - 8 4 - 5 - 7 4 - 6 - 8 5 - 6 - 8
4 - 5 - 8
5 - 7 - 8 6 - 7 - 8
a) Probability is 17/30
b) There is only 1 right triangle 3 - 4 - 5....probability is 1/30
