Let E be the set of even integers and let OO be the set of odd integers. Suppose that a computer is programmed to input a sequence of elements of E and output a sequence of elements of O according to some rule. You run a test of this program using 12,6,8,10,212,6,8,10,2 as input, and the computer outputs 81,9,25,49,181,9,25,49,1. What rule does the computer appear to be using?

The following table shows the number of new (single-unit) houses started, in thousands, in the different regions of the United States during 2012-2014. Take S to be the set of all housing starts represented in the table, and label the sets representing the housing starts in each row and column as shown (so, for example, N is the set of all housing starts in the Northeast during 2012-2014). 2012 (4) 2013 (8) 2014 (C) Total Northeast (N) 50 60 OBOM' OBUM' OANM' OcnM O AUM Compute its cardinality. thousand 50 160 Use symbols to describe the given set. Midwest South (M) (S) 90 100 110 300 280 330 350 960 West (W) 110 130 150 390 Total 530 620 660 1,810 the set of housing starts in 2013 excluding housing starts in the the Midwest

Suppose we want to choose 2 colors without replacement from 5 colors red, blue, green, purple, and yellow. How many ways can this be done, if the order of choices is relevant? How many ways can this be done if the order of choices is not relevant?

14! / 8!6!