The traffic that makes a left turnat an intersection consists of two types of ve

Question

The traffic that makes a left turnat an intersection consists of two types of vehicles, Type A andB. A type A vehicle is twice the length of the type B. THe left turn lane can accommodate ten vehicles of type B, five oftype A. List the set of all possible combinations of vehicleswaiting for a left turn at the intersection. The traffic that makes a left turnat an intersection consists of two types of vehicles, Type A andB. A type A vehicle is twice the length of the type B. THe left turn lane can accommodate ten vehicles of type B, five oftype A. List the set of all possible combinations of vehicleswaiting for a left turn at the intersection.

Explanation / Answer

A combination is a way of picking a certain number of objects inwhich the order does not matter. As opposed to permutations,where the order does matter. For example, if you wanted tofind the number of combinations that would result in a royal flushin poker (Ace, King, Queen, Jack, Ten of the same suit) in a 5 cardhand, there would be four combinations, one for each suit. For the number of permutations, there would be 4*5*4*3*2*1 =480 permutations because for each combination there are 5! =120 ways to order the five cards. So, the set of combinationswould be {{A, A, A, A, A}, {A, A, A, A, B, B}, {A, A, A, B, B, B,B}, {A, A, B, B, B, B, B, B}, {A, B, B, B, B, B, B, B, B}, {B, B,B, B, B, B, B, B, B, B}}.

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