Hey guys im studying for a math exam and was wondering if anyone has some easy techniques to remember in what kind of scenario to use these equations. These are I believe called multiplication rules.
$n^r$
$P(n,r)$
and $nCr$
the kinds of question i'd get ask in my exam would be like
(a)How many different four digit positive integers are there?
(b) How many use only the digits 1, 2, 3, 4, 5, 6 (repetitions allowed)?
(c) How many of those in (b) have no repeated digits?
(d) If a four digit positive integer is chosen at random (using any digits), what is the probability that it contains no repeated digits?
Note: i am not looking to find the answer to these questions, I'm simply looking for a way to identify when to use what multiplication rule. Thankyou.
The first rule the number of different sequences that can be formed by selecting 1 object of $n$ objects from a set of $r$ bins (e.g. if you have red/blue/green socks, jeans/slacks, and a white/black/green shirt, then there are 3x2x3 = 18 outfits you can make).
The second is the number of unique sequences of length $r$ you can make from $n$ objects (order matters, so abba $\neq$ baba$
The third is the number of different groups you can make by taking r objects from n objects. It only cares about which objects you choose, but not their order.