Question

Does anyone know why the notation for permutation/combinatorics is "n" choose "r"?
Were these letters selected arbitrarily?

Answer 1

or "n" choose "k" as is used in some circles?

Answer 2

n is used as a counting number a lot in algebra, as for r, I'm not sure.

For example "What is the nth term in a sequence?"

Answer 3

Why is this bothering you?

Answer 4

not so much bothering as just trying to remember what variables stand for~

Answer 5

but thank u for your insight about "n"

Answer 6

In the permutations rule n is the number of different items, and r is the number of those items.

Answer 7

n is total amount of choices.
r is the amount of things you are choosing.

for a 4 digit PIN number, how many combinations are there?

n = 10
r = 4

Answer 8

10!
----
4!(10-4)!
right?

Answer 9

for a 4 digit PIN the answer would be 10^4, since there are no restrictions on the digits you can use; you can have repeating numbers and thats ok.

Answer 10

Joemath is correct.

Answer 11

nCr is used when you need the number of combinations of something, where order isnt important. For example, lets say I have a box full of 10 different stuffed animals, and im going to pick 3 to put on my desk. If i pull out a bear, penguin, and dog, thats the same result ans picking a penguin, dog, and bear. Order is not important, it leads to the same result. so the answer would be 10C3:
\[\left(\begin{matrix}10 \\ 3\end{matrix}\right) = \frac{10!}{3!(10-3)!} = \frac{10*9*8}{1*2*3} = 120\]

Answer 12

ok i see that

Answer 13

that's right, i forgot i used the equation not allowing for repetition

Answer 14

If order is important , you use the permutation instead. For example, you have 10 people running a race, and you want to count then number of ways 1st, 2nd, and 3rd place medals can be given out. If Sally, Billy, and Sue got 1st, 2nd, and 3rd respectively, thats different than Billy, Sue, and Sally getting 1st, 2nd, and 3rd. so you use 10P3:
\[\frac{10!}{(10-3)!} = 10*9*8 = 720\]

Answer 15

good examples! thanks

Answer 16

what joemath314159 is correct