Q1 how many subsets of a set with 100 elements have morethan one element ?
q2 how many strings of four decimal digits
a) do not cantain the same digit twice?
b) end with even digit ?
c) have exactly three digits that are 9s ?

A set of elements has possible subsets, where two classes of those sets are the empty set (1) and all the possible singleton sets (). So a set of elements has possible subsets with more than one elements. For Q1 take .

Q2a. Assuming not containing the same digits twice also includes not numbers with three or four of the same digit, and assuming digits are chosen from the usual 0-9, there are



possible strings.

Q2b. The first three digits can be chosen freely from 0-9, while the last digit has to be one of 0, 2, 4, 6, or 8. This means you have



possible strings

Q2c. Any such string will take the form , , , or , where has 9 possible choices (0-9 excluding 9, since we want exactly three 9s in any such string). So there are



possible strings.