In Molitoris' GRE Practice book, Test 2 Problem 22, the reader is asked to find the probability of finding n particles of N in a subvolume of .

The an approximation to the answer is , which the solution tells you is , but I don't know how I would calculate that value in 1.5 minutes. Brute force, Taylor expansion, and limits seem to be too slow and/or unwieldy to use on the test. Any help would be appreciated.