If you have six objects, how many different combinations exist, i.e A + B, A + B +C etc?

Answer 1

If order is important (A + B is different to B + A)

6 of one object
6 * 5 = 30 of two objects
6 * 5 * 4 = 120 of three objects
6 * 5 * 4 * 3 = 360 of four objects
6 * 5 * 4 * 3 * 2 = 720 of five objects
6 * 5 * 4 * 3 * 2 *1 = 720 of six objects
Total of 1956 different combinations

If order is not important (A + B is identical to B + A)

6 of one object
(6 * 5)/(2 * 1) = 15 of two objects
(6 * 5 * 4)/(3 * 2 * 1) = 20 of three objects
(6 * 5 * 4 * 3)/(4 * 3 * 2 * 1) = 15 of four objects
(6 * 5 * 4 * 3 * 2)/(5 * 4 * 3 * 2 * 1) = 6 of five objects
(6 * 5 * 4 * 3 * 2 * 1)/(6 * 5 * 4 * 3 * 2 * 1) = 1 of six objects
Total of 63 different combinations

Wolf: unless it allows a combination of 0 elements, you need to subtract 1 from 2^6 (i.e. the time when all elements are not in). So 2^6 - 1 = 64 - 1 = 63

Answer 2

The answer is 2^6=64.
Since every object can either be or not be in the combination, every object has two options to choose from when forming one combination. Mutliplying the options for each object gives us this result: 2*2*2*2*2*2=2^6=64.

Answer 3

Tom is correct.
you have to add the # of ways which you can choose 1 object out of 6 + # of ways you can choose 2 objects out of 6 + # ways that you can choose 3 objects out of 6 etc....

Answer 4

I assumed order didn't matter and I got what Tom got. I didn't do it the other way yet, and since I'm sleepy and he did it, I'll just say goodnight for now.

Hugs...

.

Answer 5

216

Answer 6

This is factorial 6 which is 720.

Answer 7

Please, believe Tom!!