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March 14th, 2011, 11:11 PM   #1
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How can I understand permutation and probability question?

Especially on probability question. I found it difficult to understand a question that asked for its probability whether using permutation or combination.

Example of final exam question:
Quote:
 Find the number of integers between 1000 and 4000 which can be formed by using the digits 1,2,3 and 4. i) if each digit may be used only once ii) if each digit may be used more than once
Is there any 'way' I can instantly understand this kind of question? Because each time I stumble upon this kind of question, I usually get confused what to used, Permutation, combination or factorial?

 March 14th, 2011, 11:27 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: How can I understand permutation and probability questio For i) we have 4 choices for the first digit, 3 for the 2nd 2 for the 3rd and 1 for the 4th: $4\cdot3\cdot2\cdot1=24$ For ii) we have 4 choices for all 4 digits: $4^4=256$
 March 15th, 2011, 01:56 AM #3 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: How can I understand permutation and probability questio Oops! You don't have four choices for the first digit; it can only be 1, 2, or 3. So you have (i) 18, and (ii) 192. The question you have to ask yourself is, "How are the valid possibilities constructed?" Can you construct them by permuting a list? Then think about permutations. Can you construct them by choosing from a list? Then think about combinations. Is it possible to select one element at a time, without any selection having an impact on later selections? Then think about a multiplication. If one selection does affect later selections, consider drawing a game tree of possibilities.
 March 15th, 2011, 05:49 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: How can I understand permutation and probability questio D'oh!

### how to know that this questio is permutation or combination

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