There are 12 paintings at an art show. Three of them are chosen randomly to display in the gallery window. The order in which they are chosen does not matter. How many ways are there to choose the paintings?A.220B.144C.1320D.36SUBMITarrow_backPREVIOUS
Question
There are 12 paintings at an art show. Three of them are chosen randomly to display in the gallery window. The order in which they are chosen does not matter. How many ways are there to choose the paintings?A.220B.144C.1320D.36SUBMITarrow_backPREVIOUS
Solution
The problem is asking for the number of combinations of 12 paintings taken 3 at a time. This is a combination problem because the order in which the paintings are chosen does not matter.
The formula for combinations is:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of options,
- k is the number of options chosen at a time,
- "!" denotes factorial, which means multiplying all positive integers up to that number.
Substituting the given values into the formula:
C(12, 3) = 12! / [3!(12-3)!] = 12! / [3! * 9!] = (12 * 11 * 10 * 9!) / (3 * 2 * 1 * 9!) = (12 * 11 * 10) / (3 * 2 * 1) = 220
So, there are 220 ways to choose the paintings. The answer is A.220.
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