A former colleague Bill Wardlaw (March 3, 1936-January 2, 2013) used to create a “Problem of the Week” for his students, giving a prize of a cookie if they could solve it. Here is one of them.
The Maryland “Big Game” lottery is played by selecting 5 different numbers in and then selecting one of the numbers in . The first section is an unordered selection without replacement (so, arrange them in increasing order if you like) but the second selection can repeat one of the 5 numbers initially picked.
How many ways can this be done?