Binomial probability

Hi… I am confused about why we use the combination formula for binomial probability… cuz we learned that combination formula is used when order is not important… so for example if we re trying to find binomial probability of getting 3 black balls from 5 draws from a bucket which contains black and white balls… we could have … bbbww wbbbw bwbwb … all of these have 3 blacks balls n 2 white ones… n each of these options is a unique draw… so order does matter here right…

The order doesn’t matter here. Three black balls could be in any order => “BBBww”, “BwBwB”, “BBwBw, “BwBBw, and etc.


i think i get it… thankyou pyng

1 Like

With all due respect, that’s not it.

The combinations formula counts all those that you’ve listed as being different, as it should. The permutations formula also counts them as different.

Suppose that the balls all have numbers: B1, B2, B3, W1, and W2. The combinations formula counts all of these the same (i.e., as one combination), whereas the permutation formula counts them as different (i.e., as twelve permutations):

  • B1B2B3W1W2
  • B1B3B2W1W2
  • B2B1B3W1W2
  • B2B3B1W1W2
  • B3B1B2W1W2
  • B3B2B1W1W2
  • B1B2B3W2W1
  • B1B3B2W2W1
  • B2B1B3W2W1
  • B2B3B1W2W1
  • B3B1B2W2W1
  • B3B2B1W2W1

Because the balls, in fact, do not have numbers (or, more accurately, even if they do have numbers we don’t care: a black ball’s just a black ball and a white ball’s just a white ball), we want to count BBBWW once, not 12 times. Hence: combinations.


Yes Sir. :blush:

1 Like