Probability of randomly drawing all numbers from a set If I draw at random from a set of 50 numbers( say 1:50), five numbers without replacing the drawn number, and then repeat this process ten times starting each 'draw' from the full set, how likely is it that I will draw every number of the set? How do I calculate this? Would it be 50( the number of 'draws') divided by 500 ( the total number from which the draws were taken) i.e.10% or is it more complicated than this?
 A: I define trial as the process of five draws. In the first trial, your chance to draw five different numbers is 100%. So, your probability will depend only on the last nine trials. In the second trial, you calculate first the probability to draw any number except the ones from the first trial, i.e 45/50. Now, as you have already six different numbers, the probability for drawing again a different number is 44/49, and so on. Since you replace after every trial all numbers, your probability of drawing in the first draw of the third trial any number that wasn't drawn before is 40/50. And then you proceed as before. At the end, you need to multiply all probabilities for each draw, because you have a logical And, i.e. you draw a number And all others before must be different from it. I calculated with R and it resulted in 2.694293e-20. The probability is almost zero!
Here is the code: 
n <- 45:1 #numerator with desired outcomes
d <- rep(50:46,9) #denumerator with possible outcomes
p <- prod(n/d) # logical 'and': multiplication
p #print the probability

