Let p(n) be the probability that a random n-digit integer has all 10 digits occurring each at least once.
Let us allow leading zeroes; e.g. 0000018274 will be included in the set of 10-digit numbers).

So p(9) is 0 , p(10) = 10!/10¹⁰ and p(1000) would be very close to 1.

a. What is the smallest n for which p(n) > 1/2?
b. >3/4?
c. >.95?