Question

While organizing a film festival, you must decide which of the 12 movies will be shown on the big screen. You only have the budget to show 5 movies on this screen, and you want to be able to tell moviegoers which order the films will be shown. In how many different ways can you show 5 of the 12 movies on the big screen?

Answer 1

The equation to calculate how many ways that "r" things can be chosen from a larger set of "n" things is:n! / [r! * (n-r)!] =
12! / (5! * 7!) =
12 * 11 * 10 * 9 * 8 * 7! / (5! * 7!) =12 * 11 * 10 * 9 * 8  / 5 * 4 * 3 * 2 =11 * 9 * 8  =792 ways

http://www.1728.org/combinat.htm

Answer 2

Answer: 792

Step-by-step explanation:

We know that the formula for the number of combinations of n things taken r at a time is given by :-

$C(n;r)=\dfrac{n!}{r!(n-r)!}$

Now, the number of combinations of 12 things taken 5 at a time is given by :-

$C(12;5)=\dfrac{12!}{5!(12-5)!}\\\\\\=\dfrac{12\times11\times10\times9\times8\times7!}{120\times7!}=\dfrac{11\times9\times8}{1}=792$

Hence, the number of different ways can you show 5 of the 12 movies on the big screen = 792