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Permutations and Combinations

Permutations and Combinations. Which is which?. Permuatation. A permutation is an arrangement of things in a certain order Factorials are used to calculate permutations ! Is the symbol for factorial. Factorial.

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Permutations and Combinations

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  1. Permutations and Combinations Which is which?

  2. Permuatation • A permutation is an arrangement of things in a certain order • Factorials are used to calculate permutations • ! Is the symbol for factorial

  3. Factorial • To calculate a factorial you multiply the number times all the whole numbers less than it until 1 • For example: 5! = 5 x 4 x 3 x 2 x 1

  4. Permutations • Example: How many ways can a softball manager arrange the first four batters in a lineup of nine players?

  5. Examples: • How many different 5-digit zip codes are there if no digit is repeated? • The chromatic scale has 12 notes. In how many ways can a song start with 4 different notes from that scale?

  6. Combinations • A combination is an arrangement of objects in which the order is NOT important. • Permutations and combinations are related! You can find the number of combination of objects by dividing the number of permutation of the entire set by the number of ways each smaller set can be arranged.

  7. Examples: In how many ways can you chose a committee of three students from the six members in student council? Customers can select three toppings from among chili, onions, cheese, mustard, or relish for their hot dogs. How many combinations of three-topping hot dogs are there?

  8. Combination or Permutation? • Decide which of the following are combinations or permutations. Then work out. • How many ways can three flute players be seated in the first, second, or third seats in orchestra? • Six children remain in a game of musical chairs. If two chars are removed, how many different groups of four children can remain?

  9. Now re-visit your test questions about arrangement • 7th grade test: #12, #22 • 8th grade test #4, #12

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