SOLUTION: A bag contains six small straws of the following lengths: 2 cm, 3 cm, 5 cm, 7 cm, 11 cm, 13 cm Three straws are drawn at random. What is the probability that a triangle can be form

To form a triangle, every pair of the three straws drawn 
must have lengths whose sum is greater than the third side.

If we choose the longest two straws, 13cm and 11cm,
the third straw can be 3cm, 5cm or 7cm.  So that's 3
successful choices.

If we choose the longest and the next to the longest,
13cm and 7cm, neither 5cm nor 3cm nor 2cm will form a triangle.
So we still have only 3 successful choices.

So that's all the ways we can choose the 13 cm straw

If we choose the 11cm and 7cm, then we can only choose 
the 5cm.  So that's another way.  So far we now have 
4 successful choices.  That's all the ways we can
include the longest two.

There is just one more successful choice with 7cm being 
the longest, namely the 5cm and the 3cm.  So that makes 
5 ways in all. 

So there are only five successful choices of three so that the 
sum of every pair of straw's lengths is greater than the third
straw's length.  They are 

1. 13,11,7 cm
2. 13,11,5 cm
3. 13,11,3 cm
4. 11,7,5 cm
5. 7,5,3 cm

There are  ways to draw any three straws.

So the desired probability is  or , choice (e).

Edwin