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There are 11 paintings at an art show. Four 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.44B.7920C.121D.330

Question

There are 11 paintings at an art show. Four 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.44B.7920C.121D.330

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Solution

The problem can be solved using the combination formula, which is used when the order of selection 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 is the product of all positive integers up to that number.

In this case, n = 11 (the total number of paintings) and k = 4 (the number of paintings chosen to display).

So,

C(11, 4) = 11! / [4!(11-4)!] = 11! / [4! * 7!] = (111098) / (4321) (since the 7! in the numerator and denominator will cancel out) = 330

So, there are 330 ways to choose 4 paintings from 11. The answer is D.330.

This problem has been solved

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