Please help me!!

Suppose that r-cylindrical shafts made by machine are selected at random from the production of the machine and their diameters and lengths measured. It is found R_{11}have both measurements with tolerance limits, R_{21}have satisfactory diameter but unsatisfactory lengths, and R_{22}are unsatisfactory as to both measurements.The total sum of R_{ij}is r. Each shaft may be regarded as a drawing from multinomial population with density,

(p_{11})^{x11}(p_{12})^{x12}(p_{21})^{x21}(1-p_{11}-p_{12}-p_{21})^{x22}for x_{ij}=0,1

having 3 parameters and the sum of all x_{ij}is 1. What are the maximum likelihood estimates of the parameters, R_{11}=90, R_{12}=6,R_{21}=3, R_{22}=1?

how am i going to derive the mle for the parameters of multinomial distribution?