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?	Select the correct option:  A) 46  B) 64  C) 164  D) 146  E) 56

Rationale: the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 12 r = 3 so , total groups is 12 c 3 = 12 ! / ( 3 ! ( 12 - 3 ) ! ) = 220 , and n = 12 - 4 = 8 r = 3 for groups without a triangle is 8 c 3 = 8 ! / ( 3 ! ( 8 - 3 ) ! ) = 56 , so , groups with at least 1 triangle = 220 - 56 = 164 answer : c
Answer: C