3.1 Permutations and combinations

• Factorial notation
• Permutations
• Combinations
• Application of permutations and combinations

• express a natural number in factorial notation
• perform permutations involving real life situations
• perform combinations involving real life situations
• apply permutations and combinations to real life situations
• explore the use of permutations and combinations in real life situations

“How are permutations used in day-to-day life?”

“Where is combination used in day-to-day life?”

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1. Factorial notation
   40 min · 1 practice tasks · quiz
   Evaluate small factorials, write a falling product as a factorial, and use 0! = 1.
2. Simplifying factorial quotients
   40 min · 1 practice tasks · quiz
   Cancel a factorial quotient down to a short product, then solve n(n - 1) = 42 for a natural number n.
3. Permutations
   40 min · 1 practice tasks · quiz
   Count ordered arrangements of r distinct objects chosen from n, first by listing and then by nPr.
4. A full line, and one fixed place
   40 min · 1 practice tasks · quiz
   Arrange n distinct objects in n places, then count again when one object is fixed at one end or at either end.
5. Combinations
   40 min · 1 practice tasks · quiz
   Count unordered selections with nCr, and see why 5C2 and 5C3 are equal.
6. From a group to its orders
   40 min · 1 practice tasks · quiz
   nPr = nCr x r!, and the edge values nC0, nC1 and nCn are 1, n and 1.
7. Which count the story asks for
   40 min · 1 practice tasks · quiz
   Decide among n!, nPr and nCr from whether order matters and whether every object is used.
8. Choose a group, then arrange it
   40 min · 1 practice tasks · quiz
   A committee of 3 from 10 is 120, and seating those 3 is another 6, giving the same 720 as 10P3.