How to calculate total chance from different simultaneous chances

5C2 is just 5!/(3!)(2!) = 120, nCr is n!/(r!)((n-r)!).
If you didn't know, you can work out the probability of activating at least once is 1 - P(not activating at all).

@Shinku: I can probably work out the answer if you give me the conditions to be fulfilled
EDIT: Ninja'd

Wisdom has 5% chance of activating.
p = 0.05
q = 0.95

Buster is 4 hits, so n = 4
If we want to work out at least one proc, work out for r = 0
4C0 (0.05)^0 (0.95)^4
= 0.8145
~81.45% chance of not triggering at all, which means 18.55% of triggering at least once per 4 hits of buster.

Also it should be nCr p^r q^(n-r), baconator25 kinda derped there.

thanks a lot, but i posted this in the rubik's cube to know how to do it myself, something relating to probability like this is prone to be useful to at least have an idea later on.

Well instead of jumping right into the formulas, try understanding how it works first.

You draw 5 cards, they can all be Hearts, Diamonds, Spades, or Clubs.
You draw the first card, it can be any of the 4.
You draw the second card, it can be any of the 4.
...
To have exactly 2 hearts, your hand will look like one of the following combinations, where X means some other suit, and H means Hearts:
- HHXXX, HXHXX, HXXHX, HXXXH
- XHHXX, XHXHX, XHXXH
- XXHHX, XXHXH
- XXXHH
A total of 10, which is the same number as 5C2 (there are 10 ways to choose a combination of 2 items from 5 unique items). The mathematical formula for finding 5C2 is, as shown above, 5!/(2!*(5-2)!), but that's just nuances that don't help with the concept.
Then you find the probability of landing one those combinations. Which means 2 successes and 3 failures, strict.

thanks, i figured that before when i said "after staring long enough at the formula", when i said that i didn't know what to do with the 5C2, it's because i literally had no idea what it meant, i haven't done any serious math in ages, so i kinda have forgotten pretty much everything (had to wiki what the ! meant, that's how serious it is)

n should be 5, since i am drawing 5 cards
r should be 2, since i am trying to get 2 successes (hearts)
p= 4/52 = 1/13
q= 12/13

nCr p^r q^(n-r)
5!/(2!)(5-2)! (1/13)^2 (12/13)^(5-2)

120/(2)(6) (1/169) (1728/2197)

(120/12) (1/169) (1728/2197)

(207360/4455516)

0.04 so this would be the answer correct?