model {
for (i in 1:4){
count[i,1:5] ~ dmulti(q[i,1:5], M[i])
q[i, 1:5] ~ ddirch(alpha[])
}
for (r in 1:5) { alpha[r] <- 1 }
}

Data:
list(count=structure(.Data=c(210,60,0,1,1, 88,641,0,4,13, 0,0,0,0,0, 1,0,0,0,1),.Dim=c(4,5)),
M=c(272,746,0,2))

node mean sd MC error 2.5% median 97.5% start sample
q[1,1] 0.7624 0.02535 7.005E-4 0.712 0.7624 0.81 1001 1000
q[1,2] 0.2196 0.02476 6.719E-4 0.1714 0.2195 0.2688 1001 1000
q[1,3] 0.003538 0.003529 1.028E-4 5.867E-5 0.002415 0.01284 1001 1000
q[1,4] 0.007214 0.00499 1.468E-4 8.039E-4 0.006233 0.01893 1001 1000
q[1,5] 0.007251 0.00527 2.114E-4 0.001039 0.005885 0.02136 1001 1000
q[2,1] 0.1183 0.01186 3.945E-4 0.09651 0.1175 0.1433 1001 1000
q[2,2] 0.855 0.0128 4.02E-4 0.8287 0.8556 0.8782 1001 1000
q[2,3] 0.001299 0.001253 3.739E-5 3.105E-5 9.616E-4 0.004576 1001 1000
q[2,4] 0.006677 0.003021 9.831E-5 0.00201 0.006286 0.01416 1001 1000
q[2,5] 0.01879 0.00513 1.508E-4 0.009865 0.01821 0.02977 1001 1000
q[3,1] 0.2025 0.1621 0.004761 0.007664 0.1608 0.6259 1001 1000
q[3,2] 0.2002 0.1604 0.004851 0.006913 0.1618 0.5696 1001 1000
q[3,3] 0.197 0.156 0.005187 0.008452 0.1574 0.5817 1001 1000
q[3,4] 0.1981 0.1626 0.004973 0.004323 0.1566 0.5921 1001 1000
q[3,5] 0.2022 0.1656 0.004872 0.008328 0.1659 0.6014 1001 1000
q[4,1] 0.2791 0.1612 0.004469 0.04289 0.2511 0.6346 1001 1000
q[4,2] 0.1449 0.1251 0.003582 0.00435 0.1044 0.4584 1001 1000
q[4,3] 0.1355 0.118 0.003442 0.003818 0.1018 0.4462 1001 1000
q[4,4] 0.1413 0.1272 0.004015 0.004763 0.1057 0.4792 1001 1000
q[4,5] 0.2992 0.1638 0.005451 0.05086 0.2767 0.6545 1001 1000