jmc

Since there are six candidates for president, the presidential candidates can be ordered in $6!=720$ ways. Likewise, there are $4!=24$ vice presidential permutations. And $5!=120$ secretarial permutations. Finally, $3!=6$ treasurer permutations. We must multiply the number of permutations for each position, since each ballot includes all the position permutations: $720\cdot 24\cdot 120\cdot 6=\boxed{12441600}$.