Question

How many combinations exist for the letters m, n, o, p, and q taken 3 at a time?

I would have thought it would have been 3! giving me 6, but that's not it.. Help? Thanks!

Answer 1

There are 5 letters total

So there are 5 choices for the first slot

5-1 = 4 choices for the second slot

and 5-2 = 3 choices for the third slot

Answer 2

10

Answer 3

Oh, right! So I do 5*4*3 giving me 60, right?

Answer 4

Which means that there are 5*4*3 = 20*3 = 60 possible ways to choose 3 letters from the 5 total

Answer 5

BUT

that's if order matters

Since order does not matter and something like

mno
mon
nmo
nom
omn
onm

are all the same, then you've over counted by a factor of 3! =3*2*1 = 6

Answer 6

So you have to divide the count of 60 by 6 to get the final answer of 60/6 = 10

So there are 10 ways to choose three items from the list of five total where order doesn't matter

Answer 7

https://www.desmos.com/calculator/ixfb9yy8fj

Answer 8

Ohhh, right. I forgot that combinations are different.. But thank you :)

Answer 9

yes if they specifically said "permutation", then order would matter

Answer 10

Oh right. Those darned specifics.. :P

Answer 11

sadly it gets confusing because a combination lock is really a permutation lock (at least to a mathematician)

Answer 12

That's beyond me.. Lol.

Answer 13

yeah it takes a while to get a good grasp of it