There are 6 people on the ballot for re
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judges. Voters can vote for any 4. Voters can choose to vote for 0, 1, 2, 3, or 4 judges. In how many different ways can a person vote?
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To solve this problem, we can use the combination formula, which is given by:
nCr = n! / (r! * (n-r)!)
where n is the total number of options (6 judges in this case) and r is the number of options we are choosing (4 judges in this case).
First, let's calculate the number of ways a person can vote for 0 judges:
6C0 = 6! / (0! * (6-0)!) = 6! / (0! * 6!) = 1
Next, let's calculate the number of ways a person can vote for 1 judge:
6C1 = 6! / (1! * (6-1)!) = 6! / (1! * 5!) = 6
Now, let's calculate the number of ways a person can vote for 2 judges:
6C2 = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = 15
Next, let's calculate the number of ways a person can vote for 3 judges:
6C3 = 6! / (3! * (6-3)!) = 6! / (3! * 3!) = 20
Finally, let's calculate the number of ways a person can vote for all 4 judges:
6C4 = 6! / (4! * (6-4)!) = 6! / (4! * 2!) = 15
Now, we can sum up all the possibilities:
1 (voting for 0 judges) + 6 (voting for 1 judge) + 15 (voting for 2 judges) + 20 (voting for 3 judges) + 15 (voting for 4 judges) = 57
Therefore, there are 57 different ways a person can vote in this scenario.