118 More counting

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• 11/8 More counting
• Things to do when counting.
• Make sure you are counting the right
  things.Start a list. If possible, finish it.
  This is called enumeration.
• Check your count. Try counting in a different
  way. Do youget the same number? Try your
  method of counting on thesame problem with
  numbers small enough that you canenumerate the
  set you are counting. Does it work there?
• Replace the numbers in your problem with
  variables. Use youmethod of counting to develop
  a formula for the answer.
• Generalize the problem and try to count again.

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Permutations of n things taken r at a
time. Combinations of n things taken r at a
time.
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Common 1 A florist has access to 12 types of
flowers and 4 types of foliage. If each bouquet
he makes requires 3 types of flowers and 2 types
of foliage, how many different bouquets can he
sell?
4
Common 9 A teacher is trying to pick 5 students
to represent her class at an upcoming school
competition. If there are 12 boys and 18 girls
in her class, in how many ways can the teacher
pick 2 boys and 3 girls to attend the event?
5
Permutations of things, some of which are
alike How many 4 letter words can be made from
the word heed? How many 3 letter words can
be made from heed?
6
Permutations of n gt n1 n2 . nr things
with n1 alike, n2 alike, ., nr alike.
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Common 3 How many ways can the letters of the
word "mississippi" be arranged?
8
Permutations of things around a circle How many
ways to arrange 4 people around a circle? Note
Twoseatings are the same if each person has the
same person on his left. General formula

9

• Books are to be chosen from a pile of 26
  encylcopedias and
• arranged onto a circular dolly. How many
  arrangements
• are possible?
• Permutations of n things taken r at a time and
  arranged around
• a circle.

10
Combination of things, some of which are
alike Given n n1 n2 nr things, n1 of
which are alike