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Understanding Permutations and Combinations: Key Concepts and Examples

Dive into the fundamentals of permutations and combinations! This guide explains permutations as arrangements of items where order matters, utilizing the counting principle and factorials to solve problems. Discover how to calculate factorials and apply them in real-world scenarios, like lining up people or mixing outfits. Learn the concept of combinations, where order doesn't matter, and explore practical examples ranging from choosing books to selecting pizza toppings. Master these essential mathematical concepts with clear explanations and engaging examples!

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Understanding Permutations and Combinations: Key Concepts and Examples

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  1. Notes 6.7 Permutations and Combinations

  2. Permutation – an arrangement of items in a particular order • Can use the counting principle or factorials to solve.

  3. Factorial: n! = n(n – 1)… • 3! = 3*2*1 = 6 • 4! = 4*3*2*1 = 24 • 0! = 1

  4. EX 1 • In how many ways can 6 people line up?

  5. EX 2 • If I have 5 pairs of shoes, 8 pairs of pants and 7 shirts, how many different outfits can I make?

  6. Number of Permutations – if all items available are NOT being used • n = items • r = items at a time

  7. EX 3 • How many 4 letter codes can be made if no letter is used twice?

  8. Combination – an arrangement of items where order DOES NOT matter

  9. EX 4 • Evaluate:

  10. EX 5 • There are 20 books on a reading list. In how many ways can you choose 4 books to read?

  11. EX 6 • A DJ wants to select 5 songs from a CD that contains 12 songs. How many 5-song selections are there?

  12. EX 7 • A pizza menu allows you to select 4 toppings at no extra charge from a list of 9 possible toppings. In how many ways can you select 4 or fewer topping?

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