M is an n-digit positive integer composed of a string of random decimal digits (no leading zero) selected from a uniform distribution. For each case below, determine the value of the smallest number of digits associated with a probability of at least 0.5 that M contains:
(A) all of the digits 0 to 9
(B) all of the 2-digit combinations 00, 01, ..., 99
(C) all of the 3-digit combinations 000, 001, ..., 999

(A) The required value of the smallest number of digits is 27.

Edited on May 10, 2024, 2:57 pm

Posted by K Sengupta on 2024-05-10 14:56:11