Permutations and Combinations
These terms are related to the business of organizing members of sets in different ways.
In elementary school math, we might say Vanessa can wear a blue shirt or white shirt with blue jeans or white jeans. How many combinations can she wear? Vanessa can wear 4 combinations:
BB, WB, BW, WW
We have 2 choices of shirts times 2 choices of jeans, or 2 x 2 = 4
Permutations are similar but in those cases the order of the members of the set is important. For example, giving cabinet member jobs to 3 politicians - we have 3 jobs (1, 2 and 3) and could have 6 permutations:
123 and 132 and 231 and 213 and 321 and 312
We have 3 x 2 x 1 = 6 permutations.
When would this ever be important in real life?
I started today's blog with a title stating there are way too many choices! What did I mean? I'm working on our kitchen. "Say no more" some of you will respond. The t-shirt choices of last week's blogs are nothing compared to the options you face in doing a kitchen...
Here are numerical values associated with some of my choices:
Kitchen sinks (1181 choices)
Undermounted (547 choices)
Stainless -> (497)
Twin Bowl (259 choices)
Width between 24-36" (215 choices)
Wall Ovens (334 choices)
27 inch wide (95 choices)
Convection (62 choices)
Single Oven (31) or Double Oven (31)
Oven alone (26) or with microwave (5)
Cooktops (486 choices)
Gas powered (280 choices)
Width between 24-36" (194 choices)
5 burners (76 choices)
Front Controls (61) or Side (15)
Bottom Freezer Refrigerator (209 choices)
Free-standing (175 choices)
Counter-depth (109 choices)
Twin Doors (57) or Single Door (52)
Width between 24-36" (92 choices)
Built-In Dishwashers (224 choices)
Width of 24" (214 choices)
Depth of 22-25" (141 choices)
Stainless inside (110 choices)
Food grinder (42) or Not (68)
Add to these choices the options in faucets, disposals, drawer and door pulls, hinges, etc. In addition to these "simple" and "well-defined" choices in "appliances" and "machinery", we will also have to decide from a virtually infinite range of paint colors, wood stains, flooring options, counter-tops and lighting.