The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability A that Tommy CANNOT form a triangle from the 3 sticks?
Choose the correct option:
A) 11/32	B) 13/32	C) 15/32	D) 17/32	E) 19/32
In order to form a triangle, the sum of two sides must be greater than the third side.   So we can choose the combination of numbers which will NOT result in a triangle.   Favorable outcomes:   1,1,4 (4&gt;1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or   1,2,4 (4&gt;1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!   1,3,4 (4=1+3): 6 ways of arriving at this   2,2,4 (4=2+2): 3 ways of arriving at this   1,1,3 (3&gt;1+1): 3 ways of arriving at this   1,2,3 (3=1+2): 6 ways of arriving at this   1,1,2 (2+1+1): 3 ways of arriving at this   Overall favourable outcomes: 30   Total outcomes:  4*4*4= 
<gadget id="calculator"> 4*4*4</gadget>
<output>64</output>
64 (4 ways of choosing a stick from each of the 3 bags)   Probability A that a triangle is not formed= 30/64 = 15/32   15/32 is the correct option here.
<result>C</result>
The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability A that Tommy CANNOT form a triangle from the 3 sticks?