Permutation of n ,not all different things, taking r at a time

Question

Please read it once again, it's not as easy as it seems.

Is there any Mathematical formula or finite approach to solve this type of problem. Eg - Find the permutation of word "MALAYALAM" taking 5 at a time.

I have written a program which can solve this type of problem ,but I couldn't found any method to do it on paper.

My programming approach - (i) Find all the combination taking r at a time

(ii) Remove duplicates from combination by sorting

(iii) Find the permutation of individual combination and then sum up, to get the answer.

Please help me, Thanks

Possible duplicate of Number of ways of forming 4 letter words using the letters of the word RAMANA — user190080, Jul 15 '18 at 13:39

true blue anil · Accepted Answer · 2018-07-15T07:43:20.210

0

Yes, there is a formula.
The word has one Y, two each of M and L and four of A

and the formula would be to find the coefficient of $x^5$ in $5!(1+\frac{x}{1!})(1+\frac{x}{1!}+\frac{x^2}{2!})^2 (1+\frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!})$

To understand why this works, you can see here

edited Jul 15 '18 at 07:43

answered Jul 15 '18 at 07:26

true blue anil

41,295

Thanks frnd ,I got it – RAHUL JAISWAL Jul 15 '18 at 14:51
You're welcome ! – true blue anil Jul 15 '18 at 19:07

Permutation of n ,not all different things, taking r at a time

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