Question

If I have 5 letters (A,B,C,D,E), and I want to form groups of three letters.
a) How many can I form? (AAA, AAB, AAC, etc)
b) How many without repeating? (ABC, ABD, etc)

Answer 1

a) thats a combination of 3 from 5..or 5 C 3

Answer 2

So 125 in the first one, and 20 in the second one. Why is it n(n-1)?

Answer 3

:/

Answer 4

If I'm not mistaken the first one is a permutation since elements are allowed to repeat. Which means the total number of three letter formations should be \(n^r=5^3 = 125\)


The second question is a combination since elements are not allowed to repeat. So I imagine that it is \(5C3\)

Answer 5

Ok, let me check :)

Answer 6

I searched an in a permutation elements cant be repeated :/

Answer 7

You should do more research on permutations.

Answer 8

So the basic formulas are \[n ^{r}\] if they can be repeated and NCr, when they cant be repeated?

Answer 9

This resource might help clear things up a bit more:
http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Answer 10

Thanks :)

Answer 11

yw

Answer 12

Yep, this helped me a lot :)

Answer 13

I am seeing that the formula of the combinations without repetition and permutation without repetition are the same. How can I know if this if a permutation or a combination? (the order matters here?)

Answer 14

They're not the same :)

Answer 15

oops, not the same, I reduce by r one more time. But how can I know in this case if it is permutation or combination?

Answer 16

(from the question?, how can I know if order matters?

Answer 17

So it is 125 and 10 :)