The greater bluffs council is having a meeting for president, vice-president, and treasurer. There are 20 candidates to choose from, and each candidate can serve at most one position. How many ways are there to elect the positions, is Mr. Jones and Mrs. Smith cannot sit on the council at the same time?
There are 20 x 19 x 18 difference possibilities = 6840
How many of these possibilities have both Smith and Jones?
There could be: S, J, x or S, x, J or x, S, J or J, S, x or J, x, S or x, J, S.
where x could be any of the other 18 persons, for a total of 6 x 18 = 108 possibilities.
Subtracting these, we get 6840 - 108 = 6732 that don't have both Smith and Jones.