Can someone explain where I can learn more about this: WWWLL --> 5!/(3!2!) = 10 Why do you divide here. I think i get the logic, but how do you know to choose 3! and 2!, and how can I know when to do this.
You arrange 5 distinct objects in 5! ways.
But if some of them are identical, you need to divide the total arrangements by the factorial of that number: Say you have total n objects out of which m are identical.
Total number of arrangements = n!/m!
e.g. Out of 5 objects, if 2 are identical, number of arrangements = 5!/2! (because we don't have as many arrangements as before now.)
Say 5 objects are A, B, C, D and D. There are 2 identical Ds.
5! gives the arrangements of 5 distinct objects(e.g. ABCDE, ABCED are two diff arrangements) but if two letters are same, ABCDD is same as ABCDD (we flipped the D with the other D). Hence the number of arrangements are half in this case: 5!/2!
Similarly, if you have 5 letters such that three of them are same and another 2 are same, the number of arrangements is given by 5!/(3!*2!) as is the case with WWWLL.
Our Combinatorics book discusses this concept as well as other GMAT relevant concepts in detail. You can take a look at it here: http://www.amazon.com/Veritas-Prep-Stat ... ds=veritas
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