In a certain city each of 25 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors or a combination of 3 colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)  Answers:
A) 7 B) 3 C) 6 D) 4 E) 5
E.5:   if we have 5 colors we can choose pairs in 5C2 + 5C3 ways = 10 + 10 and single color flags are 5. Therefore total number of flags = 25.   ANS 5.
<result>E</result>
In a certain city each of 25 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors or a combination of 3 colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)