rudra07 wrote:
Hi, thanks for the reply. It helped but I still have some questions in mind. You can help me if you kindly solve for 3 letter arrangements for letters "EELL". So the rephrased question would be: how many 3 letter arrangements are possible with "EELL"?
The concept remains the same.
An alternate way to take a look at the above problem (2 out of 4) is to pick 1 combination and see in how many ways you can permute the other places.
Lets start with 1 possible combination: EL
E_ with the '=' representing another letter. We have the choice of E,L (I can only count 2 Ls as 1 L as both of them are indistinguishable).
So number of ways to choose 'E' out of 2 Es: 1
Number of ways to choose the remaining letter: 2 (remaining E and 1 L, as both of them are same!)
Thus E_ can provide us 2 arrangements. Now, we can choose either of E or L to be the first letter and thus we need to multiply 2 arrangements obtained from E_ to complete all the possible arrangements for a total of 2*2 = 4 arrangements.
This one is straightforward as the number of repetitions is less than the total length of the string (3 in this case) required. Thus the required number of arrangements are:
4P3/(2!*2!) = 6 possible arrangements.
EEL
ELE
LEE
LLE
LEL
ELL