Quandaries and Queries


I am a parent of an eighth grader and I would like to know how to do this problem. There are 4 contestants in a bicycle race. In how many different orders can they cross the finish line?

Thanks for your help. Robert



Hi Robert,

Think about making a list of the results, in order. How many lists would you need to have one list for each possible order?

For the winner there are 4 possibilities. Regardless of who is the winner there are 3 choices for second place. Thus just to include first and second place there are

4 3 = 12

lists needed. Now third place. Again, regardless of which of the 12 possible results for first and second place you have, there are two contestants left and hence two choices for third place. Hence to include first, second and third place ther are

4 3 2 = 24

lists needed. Finally, for each list you have there is only one choice for fourth place. Thus in total you have

4 3 2 1 = 24




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