Permutations

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Permutations
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Fundamental Principle of Counting If one task
can be done x number of ways and another task can
be done y number of ways then the total number
of ways in which these tasks can be completed
together is the PRODUCT. Example A club
consists of 15 boys and 20 girls. They wish to
elect a girl as president and a boy as Vice
President. They also wish to elect a Secretary
and a Treasure who may be either a boy or
girl. ( choices for Pres)( Choices for VP)(
Sec)(Tres) 20
15 33 32
316,800 different choices
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Permutation A permutation of n distinct elements
taken r at a time is an ordered arrangement,
without repetitions, of r of the n elements. The
number of permutations of n elements taken r at a
time is denoted by Example How many three
letter combinations can be made from 26 letters
if No duplication is allowed? X
X X 1st
26 choices 2nd 25 choices 3rd 24
choices
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Factorial Notation Example In how many ways
can four coins be arranged in a row? (quarter,
nickel, dime, penny)
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Example A family of 5 consisting of the parents
and 3 children are going to be arranged in a row
by a photographer. If the parents are to be next
to each other, how many arrangements are possible?
How many other possible ways?
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Evaluate
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Using ABCDE, how many 3 letter words can be
formed if repetitions are NOT allowed?
Using ABCDE, how many 3 letter words can be
formed if repetitions are allowed?
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Group Problem

• If you have 5 signal flags and can send messages
  by hoisting one or more flags on a pole. How many
  messages can you send? (order matters)