Question

Well, I know what it's not..


Which of the following is an example of a combination?

A. Selecting a first, second and third place winner at a beauty competition.
B. Picking 4 sets of towels out of 20 different sets.
C. The number of ways 12 picture frames can be arranged on a shelf.
D. The number of ways 3 people can sit on a couch.
___

I know it cannot be option A because it is an example of a permutation. As for the others though, I have no idea.

Answer 1

C because a combination has multiple ways

Answer 2

A combination is a way of selecting several things out of a larger group, where order does not matter.

Answer 3

Thank you @misssunshinexxoxo :)

Answer 4

That I knew, but I thought C and D were similar.

Answer 5

It's a LARGE group

Answer 6

Ah large. 3 is not large haha. thanks

Answer 7

D is smaller having 3 people verses the picture frames

Answer 8

Exactly!

Answer 9

actually, I think B would be the better answer

usually, when you arrange something in a row (like picture frames or people on a couch), the order matters

Answer 10

B really wouldn't be good because picture frames and paintings have multiple combinations

Answer 11

About B, I wasn't sure if it was that one or not because it says 'different' sets.

Answer 12

for example, if we have three people, Ally Betty and Cathy sitting on a couch, then if Ally Betty and Cathy sit in the order ABC, it's different than the order BCA or ACB

Answer 13

A combination is a way of selecting several things out of a "larger group", where order does not matter.

Answer 14

remember:

permutation: order matters
combination: order doesn't matter

Answer 15

B ONLY allows 4 SETS to be chosen out of 20

Answer 16

That fact I got down. I just forgot about the 'large' group part.

Answer 17

B is the better answer:

if I pick 4 sets of towels, picking ABCD is the same as BCDA because it's the same 4 towels

Answer 18

*the same 4 sets of towels

Answer 19

C is the larger group

Answer 20

group size has nothing to do with combination vs permutation

Answer 21

hmm...

Answer 22

well, maybe think about it this way:

C and D are pretty much the same scenario with different numbers

Answer 23

Okay, that's what I thought as well.

Answer 24

alright, hopefully my explanation wasn't too confusing D:

Answer 25

Not too hard to follow, thanks :)

Answer 26

I just don't know now because D is just a larger version of C.

And A says 'different' sets.