If I have 10 numbers in a hat, what is the probability that I draw out all 10 in order of 1 through 10, 3 times in a row?

Question

Probability of doing the same thing in the same order many times in a row. 

Answer 1

Only one permutation of draws satisfies the event; # of possibilities of drawing in any order is ₁₀P₁₀ = 10!

 

P(E) = probability of drawing out numbers in order from 1 to 10 = 1/10!

 

so probability of this happening 3 consecutive times is 1/(10!)³ -- very rare.  (You get to do the computing)