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  1. No Repetition: for example the first three people in a running race. You can't be first and second. 1. Permutations with Repetition. These are the easiest to calculate. When a thing has n different types ... we have n choices each time! For example: choosing 3 of those things, the permutations are: n × n × n (n multiplied 3 times)

  2. Distributive Law. The "Distributive Law" is the BEST one of all, but needs careful attention. This is what it lets us do: 3 lots of (2+4) is the same as 3 lots of 2 plus 3 lots of 4

  3. Permutations and Combinations Worksheet Evaluate each permutation or combination (you must show the set up) : 1. 7P 3 2. 7P 4 3. 7P 7 4. 8C3 5. 8C5 ⋅ 7C3 6.7C2 Find the number of possibilities (you must show the set up). 7. The ski club with ten members is to choose three officers captain, co-captain & secretary, how many

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  4. 1. Choosing a subset of r elements from a set of n elements; 2. Arranging the chosen elements. and. Referring to EXAMPLE 1.5.6 above, Gomer is choosing and arranging a subset of 9 elements from a set of 20 elements, so we can get the answer quickly by using the permutation formula, letting n = 20 and r = 9.

  5. The number of permutations of n things taken k at a time is. (P(n, k) = n(n − 1)(n − 2)⋯(n − k + 1) = n! (n − k)!. A permutation of some objects is a particular linear ordering of the objects; P(n, k) in effect counts two things simultaneously: the number of ways to choose and order k out of n objects. A useful special case is k = n ...

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  8. Permutation and combination are the methods employed in counting how many outcomes are possible in various situations. Permutations are understood as arrangements and combinations are understood as selections. Understand the Permutations and Combinations Formulas with Derivation, Examples, and FAQs.

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