Algebra &Trigonometry: Permutations and Combinations?

Question

We just learned that PERMUTATIONS are just an application of fundamental counting priciple. We also learned that COMBINATIONS are just an application of PERMUTATIONS and the counting principle. Question: Can you say that COMBINATIONS are also just an application of the counting principle?

Answer 1

Sure, if you need to for your peace of mind. But the important difference between combinations and permutations is the fact that order doesn't matter for combinations. Permutations "overcount" when you are only concerned about combinations. In a sense, combinations represent a partial reverse-application of the counting principle upon the result of a permutation. Hope this confuses you in a good way.

Answer 2

A Permutation is the number of ways you can arrage certain objects/things with order being important.

Example: abc, acb, bac, bca, cab and cba are all permutations of the letters a, b and c.
This is a permutation of 3 letters taken 1 at a time. We could say this permutation consists of 6 arrangements.

A Combination disregards order of things.

Example:
a(bc) and a(cb) are considered to be the same combination. b(ac) and b(ca) are also considered to be the same combination. c(ab) and c(ba) are considered to be the same combination. This is a combination of 3 letters taken 1 at a time. We could say that this combination consists of 3 arrangements only.

So we define combinations in terms of permutations:

nCr = nPr / r!

where nCr is the combination of n things taken r at a time and nPr is the permutation of n things taken r at a time.

So to summarize: Combinations are permutations without regard for order.

Answer 3

permutation is basically an arrangement whereas combination is selection

Answer 4

It's really important to understand when order is important to the solution of the problem.

Answer 5

yes