Evaluating Large Factorials Many calculators or computers cannot directly calculate 70! or higher. When n is large, n! can be approximated by n 5 10K, where K 5

(n 1 0.5) log n 1 0.39908993 2 0.43429448n.

a. Evaluate 50! using the factorial key on a calculator and also by using the approximation given here.

b. The Bureau of Fisheries once asked Bell Laboratories for help finding the shortest route for getting samples from 300 locations in the Gulf of Mexico. If you compute the number of different possible routes, how many digits are used to write that number?