I am having some trouble doing these two questions any help

I am having some trouble doing these two questions, any help is appreciated.

1. Doughnut Whirl has 16 types of doughnuts this morning. If you allow repeats, how many different ways can a six-doughnut box be filled?

2. 35,001 people attended the second game of the 2004 World Series between the St. Louis Cardinals and the Boston Red Sox. Is it a certainty that at least two of those people share the same three-letter set of initials (such as JFK or LBJ)? Justify your reasoning.

Solution

1) The number of ways are given by 16x16x16...x16(6 times) = 16⁶ ways = 16777216 (Because repetition is allowed)