The different groups of 3 movies can a person rent if there are 12 movies to choose from is:
220
We know that choosing of r items out of a total given n items is given by the method of combination and the formula for the doing so is given by:
[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]
Here we have to chose 3 movies out of 12 movies.
Hence, we have n=12 and r=3
Hence, the number of ways of doing so is given by:
[tex]{12}_C_3=\dfrac{12!}{3!\times (12-3)!}\\\\\\{12}_C_3=\dfrac{12!}{3!\times 9!}\\\\\\{12}_C_3=\dfrac{12\times 11\times 10\times 9!}{3!\times 9!}\\\\\\{12}_C_3=\dfrac{12\times 11\times 10}{3\times 2}\\\\\\{12}_C_3=220[/tex]
Hence, the answer is:
220
