How many combinations can I make of this?

Question

Ok, I'm not much of a math wizz, so I need help solving this.

I have a row colored dots, blue - green - red - yellow
How many combinations can I make out of these, without them changing place at any time? example:

blue - - red -
- green - - yellow
blue - green - - yellow

and so on and so on?

thanks
-larsb

Answer 1

If you just think of each dot as a coin, imagine that you flip it. If it is heads you include it, if it is tails you don't.

That leads to 2 x 2 x 2 x 2 = 16 combinations. The big question would be if *no* dots is considered a combination. If not, then you have 15 combinations: 2^n - 1 = 15.

BGRY
BGR
BGY
BRY
GRY
BG
BR
BY
GR
GY
RY
B
G
R
Y

If you want to enumerate the combinations, you can use the formula for n choose k = n! / k! (n-k)!
4 choose 4 = 4! / 4! 0! = 4! / 4! = 24/24 = 1 way
4 choose 3 = 4! / 3! 1! = 24 / 6 = 4 ways
4 choose 2 = 4! / 2! 2! = 24 / 4 = 6 ways
4 choose 1 = 4! / 1! 3! = 24 / 6 = 4 ways

1 + 4 + 6 + 4 = 15 ways

1 way to choose four colors:
BGRY

4 ways to choose three colors:
BGR, BGY BRY, GRY

6 ways to choose two colors:
BG, BR, BY, GR, GY, RY

4 ways to choose one color:
B, G, R, Y

So either way you get the same answer: 15 ways

P.S. The first answerer forgot blue-red-yellow as a combination. There have to be 4 because you are skipping 1 color in a combination of 3 colors. And there are 4 colors to choose from.

Answer 2

First you find the combos of 1, blue, red, green, and yellow (4). Then, you find combinations of two, blue red, blue green, blue yellow, red green, red yellow, green yellow (6). Then you find combinations of 3, blue red green, blue green yellow, red green yellow (3). Then find the only combo of 4, blue red green yellow (1). 4+6+3+1=14

Answer 3

BGRY

BGR, BGY, BRY, GRY

BG, BR, BY, GR, GY, RY


11 COMBINATIONS

or if single colours count then 15