Question

How many different groups of 3 movies can a person rent if there are 12 movies to choose from?

Answer 1

Answer:

The different groups of 3 movies can a person rent if there are 12 movies to choose from is:

                            220

Step-by-step explanation:

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:

         $n_C_r=\dfrac{n!}{r!\times (n-r)!}$

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:

    ${12}_C_3=\dfrac{12!}{3!\times (12-3)!}\\\\\\{12}_C_3=\dfrac{12!}{3!\times 9!}\\\\\\{12}_C_3=\dfrac{12\times 11\times 10\times 9!}{3!\times 9!}\\\\\\{12}_C_3=\dfrac{12\times 11\times 10}{3\times 2}\\\\\\{12}_C_3=220$

               Hence, the answer is:

                      220

Answer 2

If there are 12 movies and a person can rent three, then there are 220 different combinations they can be rented in.