Number of combinations , "committees" of n
things taken r at a time:
HW: p. 14, #6, #8
A) When I first moved to NY, license plates
were 3 letters followed by 3 numbers (TKU397)
a) How many different license
plates could there be back then?
b) Now there are 7
characters--there
is still some pattern, but I expect eventually there won't be.
How
many plates can there be if any of the 7 characters can be any letter
or
any digit?
c) Can you count "exactly
3 letters, together, but anywhere in the list" (ACD2355, 2ACD355,
etc.).
?
**d) I'm not sure what the
present patterns are, but there seem to be clumps of letters and
digits.
Observe in the parking lot(s) and see if you can see the likely
structures
(not counting vanity plates.) Can you count how many,
if your analysis of the structures is correct?
B) Ann, Betty, Carol, Xavier and Zane are going
to the movies. They want to sit Girl, Boy, Girl, Boy, Girl.
How many possible ways are there to do this?
How many ways if Ann and Xavier refuse to sit
next to each other? (You'll need a tree, or a list...and/or a trick.)
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