Welcome back to the Maine Page! This year, all of our problems are going to involve topics covered in the five annual Maine Association of Math Leagues meets. New problems will be posted every week after the results of the first meet are posted on www.maml.net. Until then, here's a little problem to hold you over:

Suppose that A, B, C, and D are real numbers such that the following matrix equation holds true:
 

Determine the value of the following determinant:

 

Draw six cards from a standard deck of 52 playing cards without replacement. How many [u]distinct[/u] ways can you choose these six cards so that:

1) The first card drawn is a spade,
2) the second card drawn is also a spade,
3) the third card drawn is a club,
4) the fourth card drawn is a diamond,
5) the fifth card drawn is a red card (either a diamond or a heart), and
6) the sixth and final card drawn is an ace?