MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks
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Lesson 11Permutations
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Consider the possible arrangements of the letters
a, b, and c.  List the outcomes in the sample
space. If the order is important, then each
arrangement is a permutation of the three letters
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Consider the possible arrangements of the letters
a, b, and c.  List the outcomes in the sample
space. If the order is important, then each
arrangement is a permutation of the three letters

• Outcomes in the sample space.
• abc    acb    bac     bca    cab    cba
• There are six permutations.

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Permutation FormulaUse when the item
possibilities are all different.n number of
available items or choicesr the number of items
to be selected    Sometimes this formula is
written P(n,r).
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If n 5 and r 2, what is the value of 5P2?
The symbol 5P2 means the number of permutations
of 5 items taken 2 at a time. 
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If n 5 and r 2, what is the value of 5P2?
The symbol 5P2 means the number of permutations
of 5 items taken 2 at a time. 

• A permutation of 5 objects taken 2 at a time is
  equal to . . .

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If n 5 and r 2, what is the value of 5P2?
The symbol 5P2 means the number of permutations
of 5 items taken 2 at a time. 

• A permutation of 5 objects taken 2 at a time is
  equal to . . .

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How many permutations are there for the letters
in the word, BANANA?First, notice there are six
total letters of which the A is repeated 3 times
and the N is repeated 2 times. The number of
permutations is equal to . . . . 
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How many permutations are there for the letters
in the word, BANANA?First, notice there are six
total letters of which the A is repeated 3 times
and the N is repeated 2 times. The number of
permutations is equal to . . . . 

• There are six letters in BANANA (6!).The A
  repeats three times (3!)and the N repeats two
  times (2!).There are 60 permutations.

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How many permutations are there for the letters
in the word, BANANA?First, notice there are six
total letters of which the A is repeated 3 times
and the N is repeated 2 times. The number of
permutations is equal to . . . . 

• There are six letters in BANANA (6!).The A
  repeats three times (3!)and the N repeats two
  times (2!).There are 60 permutations.

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How many permutations are there for the letters
in the word, HAPPY?Remember to ask yourself, how
many total letters are there?  How many letters
are repeated? How many times is each letter
repeated?  
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How many permutations are there for the letters
in the word, HAPPY?Remember to ask yourself, how
many total letters are there?  How many letters
are repeated? How many times is each letter
repeated?  

• There are five letters in HAPPY (5!).The P
  repeats two times (2!).There are

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How many permutations are there for the letters
in the word, HAPPY?Remember to ask yourself, how
many total letters are there?  How many letters
are repeated? How many times is each letter
repeated?  

• There are five letters in HAPPY (5!).The P
  repeats two times (2!).There are

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1) Calculate the value of 7P3
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1) Calculate the value of 7P3

• A permutation of 7 objects taken 3 ata time is
  equal to . . .

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1) Calculate the value of 7P3

• A permutation of 7 objects taken 3 ata time is
  equal to . . .

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2) Calculate the value of 9P4
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2) Calculate the value of 9P4

• A permutation of 9 objects taken 4 at a time is
  equal to . . .

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2) Calculate the value of 9P4

• A permutation of 9 objects taken 4 at a time is
  equal to . . .

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How many permutations are there for the letters
in the word, STATISTICS?
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How many permutations are there for the letters
in the word, STATISTICS?

• There are ten letters in STATISTICS (10!).

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How many permutations are there for the letters
in the word, STATISTICS?

• There are ten letters in STATISTICS (10!).
• The S repeats three times (3!),the T repeats
  three times (3!), and the I repeats two times
  (2!).

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How many permutations are there for the letters
in the word, STATISTICS?

• There are ten letters in STATISTICS (10!).
• The S repeats three times (3!),the T repeats
  three times (3!), and the I repeats two times
  (2!).

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Fini!