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If i calculate combination of word "ball" using below formula (consider r as 2, I am selecting 2 letters)

C(n,r)=n!/r!(n−r)!

which return me 6 but actual combination is 4{ba,bl,al,ll}

so can anyone tell me! how to find combination of word which contains duplicate letters?

RobPratt
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User5678
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  • Hint: if there are $n$ copies of the same letter $k$, then there are $n\choose 2$ ways to make the word "$kk$". – AKemats Feb 22 '22 at 14:53
  • It depends on the specific examples you are looking at whether or not there is an easier approach... here, we just say we look for combinations from bal and then recognize that there is one additional combination we are interested in for a total of $\binom{3}{2}+1=3+1=4$. For the more general problem, it can get quite tedious to write down a generic formula but I recommend stars-and-bars along with inclusion-exclusion – JMoravitz Feb 22 '22 at 14:58
  • @JMoravitz there's generic way to solve this kind of duplication problem in permutation https://math.stackexchange.com/questions/1424380/permutations-with-repeating-letters . don't we have for combination?? – User5678 Feb 22 '22 at 15:13
  • I already linked a duplicate above. Check the duplicate and if you still need clarification then say so. Further, the question you linked was where we looked at using all of the letters, not just some of them, which makes it a different question than yours. – JMoravitz Feb 22 '22 at 15:14

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