How many plate numbers can be created in California format DLLLDDD, where D stands for digit and L stands for letter? What if no repetitions are allowed in the digits?
A zip code consists of 5 digits. If the first cannot be the digit 0, how many zip codes can be generated?
How many letter arrangements can be made from the letters of the word Iowa? How about from the letters of Connecticut?
How many 5-card poker hands are there? (A regular deck has 52 cards).
Assuming that you can only move to the right or down, in how many ways
can you get from the top left point to the bottom right one along the
depicted grid?
If you need to split a class of 32 students in 8 groups of 4, in how many ways can you do it?
If a student is required to solve 8 out of 10 assigned problems, how many choices does she have? What if the first 4 problems are mandatory?
How many actual $n$ digit numbers exist? What if no two consecutive digits can be the same? How many numbers with at most $n$ digits exist? Numbers are to be understood as actuall numbers: 1 is a one digit number but 001 is not an actual number and certainly not a 3 digit number.
A total of 6 people need to be selected from a set of 10 twins of different families (20 people total). How many choices are there, if it is not allowed to select two siblings?
A total of 8 representatives need to be chosen from a group of 40 students, of which 24 are female and 16 are male. In how many ways can this be done? What if we require that there be at least 3 female and 3 male representatives?