There are 40 students in our combinatorics class. Use combinatorial principles to compute the probability that at least two people in class have the same birthday (assume 365 days in a year)...

100% * summation from i=2 to 40 of ((40 choose i) * (1/365)^i * (364/365)^(40-i))

is equal to (by the binomial theorem)

100% * ((1/365 + 364/365)^40 - (40 choose 0) * (1/365)^0 * (364/365)^40 - (40 choose 1) * (1/365) * (364/365)^39)

= .546%