In this study, we derived new formulations for the first and second order inclusion probabilities of a ranked set sample in a finite population setting. Gokpmar and Ozdemir (2010) developed a formula to calculate the first order inclusion probabilities. However, the formula given in this study is much easier than the one given by Gokpmar and Ozdemir (2010). Second order inclusion probabilities are computed based on the formulas which are used for the calculation of first order inclusion probabilities. Also, we give a numerical example to show the calculation of the formulas and Matlab codes which give first and second inclusion probabilities for any set and population sizes.