Section 11'2 Permutations and Combinations

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Section 11.2 Permutations and Combinations
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• Factorial
• n! n(n-1)(n-2)321
• Permutations
• A permutation is an arrangement of objects in a
  certain order.
• Permutation Formula for Distinct Objects

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• Example A university Volleyball team consists of
  6 players whose position are ranked 1 through 6.
  If a coach has 10 players from which to choose,
  how many different teams can the coach select?

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• Example The Kentucky Derby had 16 horses entered
  in the race. How many different finished of
  first, second, third, and fourth place were
  possible?

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Applying Several Counting Techniques

• Example Five women and 4 men are to be seated in
  a row of 9 chairs. How many different seating
  arrangements are possible if
• (a) there are no restrictions on the seating.
• (b) the women sit together and the men sit
  together

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Permutations of identical objects

• The number of distinguishable permutations of n
  objects of r different types, where k1 identical
  objects are of one type, k2 of another, and so
  on, is given by

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Example

• How many distinct ways can the letters of the
  word MISSISSIPPI be arranged?
• INDIANA
• SET
• ANA
• OHIO
• ILLINOIS

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• Example If 7 identical dice are rolled, find the
  number of ways two 4s, one 5, and four 6s can
  appear on the upward faces.

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Combinations

• A combination is a collection of objects for
  which the order is not important.
• Combination Formula C(n,k)P(n,k) / k!
• Example A basketball team consists of 12
  players. In how many different ways can a coach
  choose the five starting players, order is not
  considered?

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• Example A committee of five is chosen from 7
  math majors and 6 economic majors. How many
  different committees are possible if the
  committee must include 2 math majors and 3
  economic majors.

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Counting Problems with Cards

• From a standard deck of playing cards(52 cards),
  five are chosen. How many five-card combinations
  contain
• Five hearts?
• Five cards of the same suit
• 4 kings
• 3 kings and 2 Aces