The Wireless Sensor Networks are energy constrained and are normally low cost and low power devices. These nodes are deployed over a specific area for specific goals. Due to energy and memory constraints, secure communication among these sensors is challenging management issue. In order to ensure security, proper connectivity among nodes and resilience against node capture, the authors propose a scheme called as Random Pre-Key distribution scheme which takes advantage of the binomial key pattern while creating and distributing keys. The value of keys would develop the number of patterns, which is given by the binomial distribution, which would be helpful in maintaining a key pool which is all though random in nature and following a pattern leads to more probability of network connection links.