We are using a 12-word scheme BIP-39 mnenemonic key generating scheme that creates an entropy of 128-bit that is then used to generate a seed that in turn derives a private key for the user. It chooses randomly 12 words out of 2048.
There are $2048^{12} = 5.444518 \cdot 10^{39}$ combinations that form the entropy for the seed.
This scheme allows duplicate words. Some users are irritated by that and write emails to support and I wonder how much entropy would get lost by only allowing unique words.
That would be $\frac{2048!}{(2048-12)!} = 5.271538 \cdot 10^{39}$ variations.
In conclusion the latter solution has only $\frac{5.271538 \cdot 10^{39}}{5.444518 \cdot 10^{39}} \approx 96.8\% $ the number of possible seeds than the non-unique one.
Is that mathematicallly correct and is that a neglectible hit on security given the increase in user friendliness?