Text non-text classification is an important research problem in the domain of document image processing. Undesirably, this is an almost ignored research topic, particularly, when we consider the unconstrained offline handwritten document images. For text non-text classification, many times researchers employ high dimensional feature vectors, which not only increase the computation time and storage requirement, but also reduce the classification accuracy due to the presence of redundant or irrelevant features. Here lies the application of some feature selection (FS) algorithms in order to find out the relevant subset of the features from the original feature vector. In this paper, our aim is two-fold. Firstly, application of coalition game based FS technique to find out an optimal feature subset for classifying the components present in a handwritten document image either as text or non-text. Secondly, five variants of a popular texture based feature descriptor, called Local Binary Pattern (LBP), along with its basic version are fed to the FS module for identifying the useful patterns only which can pinpoint the regions of an image as most informative in terms of the said classification task. To the best of our knowledge, the approach is completely novel where coalition game based FS technique is applied for locating the feature-rich regions to be used for text non-text classification. For experimentation, we have prepared an in-house dataset along with its ground truth information which consists of 104 handwritten engineering class notes as well as laboratory copies that include handwritten and printed texts, graphical components and tables etc. Experimental outcomes confirm that the proposed approach not only helps in reducing the feature dimension significantly but also increases the recognition ability of all six feature vectors.