Combining multiple information sources such as streams (with different features) and multi modal data has shown to be a very promising trend, both in experiments and to some extend in real-life biometric authentication applications. However, combining too many biometric systems (base-experts) will also increase both hardware and computation costs. Conventional way to selecting a subset of optimal base-experts out of $N$ is to carry out the experiments explicitly. There are $2^N-1$ possible combinations. In this paper, we propose an analytical solution to this task using weighted sum fusion on normalised scores (zero-mean and unit variance). The algorithm depends only on how accurately one can estimate the covariance matrix of the actual test data. The proposed algorithm has a complexcity that is additive between the number of examples and the number of possible combinations while the conventional approach is multiplicative between these two terms. Hence, our approach is more efficient. It was tested on the BANCA multi-modal database. Experimental results showed that such an algorithm is a viable solution