1. The problem statement, all variables and given/known data 50 students live in a dormitory. The parking lot has the capacity for 30 cars. If each student has a car with probability 12 (independently from other students), what is the probability that there won't be enough parking spaces for all the cars? 2. Relevant equations P(A) = P(B)P(C) Binomial: C(n k) Pk(1-p)n-k Pascal's: C(k-1 m-1) Pm(1-p)k-m 3. The attempt at a solution So the difference is in the coefficient, clearly, and i'm wondering which one to use in this circumstance. The first time i did it, I chose the Binomial because it looks like a classic "What's the probability of this many trials having successes"? type of thing, but what if you defined the problem as "what's the probability of taking 49 trials, and getting 29 successes (kids having cars for the parking lot) and then on the 50th recieving a pass. I chose 29 successes because we are tasked to find the chance of having enough spaces, not more. The difference may be negligible when you do the factorials. After all, the middle numbers will all be the same, just the ones on the ends will be slightly altered, but I really do not see the difference in use between these two formulas. It sounds like two mathematical perspectives of the same thing.