In

probability theory, the

**coupon collector's problem** describes the "collect all coupons and win" contests. It asks the following question: Suppose that there are

*n* coupons, from which coupons are being collected with replacement. What is the probability that more than

*t* sample trials are needed to collect all

*n* coupons? The mathematical analysis of the problem reveals that the

expected number of trials needed grows as

*O*(

*n*log(

*n*)). For example, when

*n* = 50 it takes about 225 samples to collect all 50 coupons.

I am a bit confused by this

50log(50) =

**84.9485002**
how do i get 225?