A custom calculation script that you can use for the total field could be like:
// Custom calculation script for TOTALMEETINGS field
(function () {
// Initialize variables
var i, count = 0;
// Loop through the dropdowns, increment counter if item is selected
for (i = 0; i < 10; i += 1) {
count += getField("COMMITTEE" + i).value === " " ? 0 : 1;
}
// Set this field value to the count
event.value = count;
})();
This assumes the entry that looks blank is really a single space.