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Permutations and Combinations... Does Order Really Matter?

Permutations and Combinations... Does Order Really Matter?. Dr Subha Anantharaj. Permutations. " The key to the safe was 472." a. Give any two choices with the same numbers 4,7,and 2 b. Do you think the safe would open with that?. Permutations and Combinations.

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Permutations and Combinations... Does Order Really Matter?

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  1. Permutations and Combinations... Does Order Really Matter? DrSubhaAnantharaj

  2. Permutations "The key to the safe was 472." a. Give any two choices with the same numbers 4,7,and 2 b. Do you think the safe would open with that?

  3. Permutations and Combinations An arrangement or listing in which order or placement is important is called a permutation. Simple example: “combination lock” • Give an example to show that order is important. • Give your reason.

  4. Combinations "My fruit salad is a combination of apples, grapes and bananas." Do we care about the order ? Explain

  5. If the order does matter - What is it called?--------------------- If the order does not matter – What is it called? --------------------------- To help you to remember, think "Permutation ... Position"

  6. A permutation is an ordered arrangement of the elements . • Let S = {a, b, c} • a, b, c is a permutation of S • a, c, b is a different permutation of S. 1.Give the other possible permutation which you can find Total permutation is ---------- . 3! = ---- * ------- * -------- .

  7. Factorial (symbol: !) just means to multiply a series of descending natural numbers. • Examples: • 4! = 4 × 3 × 2 × 1 = 24 • 6! = • 5! =

  8. Permutations of “ n ” objects In how many ways can a car dealer arrange his TEN new cars in the show room? The number of permutation is =

  9. In how many ways can Bianca,John,David,and Grace stand in row?

  10. The starting lineup for a baseball team consists of nine players how many different batting orders are possible using the starting lineup?

  11. Permutations of “n “ objects taken “r” at a time The manager of a coffee shop needs to hire two employees, one to work at the counter and one to work at the drive-through window. Sara, Megen, Tracy and Jeff all applied for a job. How many possible ways are there for the manager to place the applicants? Counter Drive-Through Outcomes Sara Megen Tracy Jeff

  12. 4P2just means to multiply a series of descending natural numbers starting from 4 up to 2 numbers. Examples: 4P2= 4 × 3 = 12 5P2= 8P3= 7P2 = 6P4=

  13. There are 8 teams competing for the 3 top places in the basket ball standings. How many arrangements of the top 3 places are possible? 1 st place 2 nd place 3 rd place Choices : ------------- * ------------ * ----------- = ---------------------------- possible arrangements

  14. There are 20 empty lockers. Five new students are to be assigned lockers. How many ways could they be assigned lockers ? Choices : ------------- * ------------ * ----------- *------------ * -------- = ---------------------------- possible arrangements

  15. How many 4 –letter sequences can be made from the letters in the word FORESAW? Choices : ------------- * ------------ * ----------- * ----------- = ---------------------------- possible arrangements

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