In a particular biological structure there are five distinct proteins. Call the proteins A, B, C, D, and E. Linear strands of these five proteins in some orders are healthy and not dangerous; however, there are some orders which prove very dangerous and most likely lead to serious diseases. The top of the strand is always distinguishable from the bottom of the strand. The dangerous line-up of proteins occur if B is not at the top of the strand or if D is not at the bottom of the strand. How many strand orders are possible that result in a safe strand? Hint: Consider the total number of orderings without regard to the B and D order con- straints. Reduce that number by the number of orderings that violate the B constraint and then reduce this number further by the number of orderings that violate the D constraint. Remember to be careful about double counting