Natwerk Designs

I can make any combination out of 120 unique items. How many possible combinations are there? formula please.?

I have a drawing that has 120 different layers. I can show any number of layers I want, from just 1 at a time or all 120 at once. So how many possible combinations of the layers are there? Can you tell me how you would go about working this out, e.g. show a formula/explanation.

Public Comments

1. You would do 120! or 120x119x118 and so on. all the way down to 1. Since 0 times anything is zero.
2. Answer: [2^(120) - 1] {Read it as (2 raised to 120) - 1} Explanation: From 120 different layers, you want to select either 1, or 2, or 3, ------ or all 120 => the combination selection is = C(120, 1) + C(120, 2) + C(120, 3) + ----- + C(120,120) ------(1) We have by property of combination coefficients, C(n,0) + C(n,1) + C(n,2) + --------- + C(n,n) = 2^n As C(n,0) = 1 C(n,1) + C(n,2) + --------- + C(n,n) = 2^n - 1 Substituting this (1) for n = 120 the answer is: [2^(120) - 1] {Read it as (2 raised to 120) - 1}
3. That is equivalent to having 120 switches, each of which has two possible positions, on or off. The number of possible combinations is 2^120. This number includes the possibility of all layers being turned off, leaving only a blank screen.
4. As others have suggested, take the factorial of 120. The symbol for the factorial function is an exclamation mark (!). This symbol tells you to multiply each preceding number. In this case, multiply 120 by 119, then 119 by 118 until you reach 1. With the help of the calculator, you are able to see that it is tedious to get the answer from pencil and paper.
5. have you never gone through the theory of probability (it is depending on situation that how much parts will be in combination)