I am voting in a state election. There are 6
candidates for governor, 4
candidates for lieutenant governor, 5
candidates for the state house of representatives, and 5
candidates for the senate. In how many different ways can I fill out a ballot if I vote once for each office?
To find out the number of ways to fill out the ballot, we need to multiply the number of choices for each office.
Total number of ways to fill out the ballot = number of choices for governor x number of choices for lieutenant governor x number of choices for state house of representatives x number of choices for senate.
Therefore,
Total number of ways = 6 x 4 x 5 x 5 = 600.
So there are 600 different ways to fill out the ballot if you vote once for each office.