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

There is a theorem which says that number of sequences $(x_1, \ldots, x_k, \ldots, x_n)$ where $x_k$ can be choosen in $m_k$ ways, $k = 1, 2, \ldots, n$ is equal to $m_1 \cdot m_2 \cdot \ldots \cdot m_n$.

I'm looking for a proof (or proofs) and official name of this theorem.

Thank you for your help.

share|cite|improve this question
sometimes called the fundamental theorem of counting – yoyo Aug 12 '11 at 20:43
Also called the Chinese menu principle, the multiplication rule, and the product rule. Since there’s no body that rules on such things, there cannot be an official name; there is merely common usage. It’s pretty obvious for $n=2$, and from that it follows by induction for larger $n$. – Brian M. Scott Aug 12 '11 at 20:51
I have the most important part - name of the theorem.Thank You. – exTyn Aug 12 '11 at 21:10
I know it as the Product Rule: if one event can occur in $n$ different ways and a second event can occur in $m$ different ways, then the total number of ways in which both events can occur is $nm$. See this previous answer. – Arturo Magidin Aug 12 '11 at 21:42
Unfortunately, "product rule" in another context means $(fg)'=fg'+f'g$. – Gerry Myerson Aug 12 '11 at 22:19

The following names were given in the comments:

  1. Fundamental theorem of counting

  2. Chinese menu principle

  3. Multiplication rule

  4. Product rule

share|cite|improve this answer

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.