Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For a n-element set, how many ways to divide the set to a combination of subsets?

For example, for the set {1, 2, 3}, there would be 5 ways to divide:

{1, 2, 3}
{1}, {2, 3}
{2}, {1, 3}
{3}, {1, 2}
{1}, {2}, {3}

For the n-element set, I thought it would be


, because imagine dividing as drop n balls to n indistinguishable boxes. But apparently, it is incorrect in the case n=3 .

share|cite|improve this question
up vote 8 down vote accepted

You want the Bell numbers --- link to Wikipedia entry.

share|cite|improve this answer
Thanks a lot. Sorry, I'm a new user in the math stackexchange, so I can't vote up your answer. – Sapience Oct 9 '12 at 1:15

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.