A box has 12 shapes; 3 circles, 5 squares, and 4 triangles. How many groups of 3 shapes can be made with at least 1 triangle?
Choose the correct choice from the following answers
A) 46  B) 64  C) 164  D) 146  E) 56
The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the 164ombination Formula: n164r= n!/r!(n-r)!   n = 12   r = 3   So, total groups is 121643 = 12!/(3!(12 - 3)!) = 220, and   n = 12 - 4= 
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
8   r= 3   for groups without a triangle is 81643 = 8!/(3!(8 - 3)!) = 56,   so, groups with at least 1 triangle = 220 - 56= 
<gadget id="calculator">220 - 56</gadget>
<output>164</output>
164   Answer: 164
<result>C</result>
A box has 12 shapes; 3 circles, 5 squares, and 4 triangles. How many groups of 3 shapes can be made with at least 1 triangle?