Problem 44
Question
Suppose you are asked to list, in order of preference, the three best movies you have seen this year. If you saw 20 movies during the year, in how many ways can the three best be chosen and ranked?
Step-by-Step Solution
Verified Answer
There are 6,840 ways to choose and rank the three best movies out of 20.
1Step 1: Determine the total number of movies
There are 20 different movies to choose from.
2Step 2: Calculate the permutation
There are 3 movies to be chosen and ranked. The formula for permutations is \( P(n,r)=n(n-1)(n-2)...(n-r+1) \) where n is the total number of options (20 movies) and r is the number of options chosen (3 movies). Plugging in the values, the formula becomes: \( P(20,3)=20*19*18 \) which equals 6,840.
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