Question

While attending a film festival you decide that there are 13 movies that you are interested in seeing. However, you only have time to see 7 movies. In how many different ways can you watch 7 of the 13 movies?

Answer 1

is it 13

Answer 2

It is a lot lot more than 13.

This is combination. Choose 7 out of 13.
\[\left(\begin{matrix}7 \\ 13\end{matrix}\right)\]
The above notation is common for this problem.

Lets say you have never seen the above and let us only use logic ( our brain ) to solve this problem.

Answer 3

So you decide that you wanna see a certain movie.
There are 13 to choose from so there can be 13 ways to choose the first one.
Now you decide on the second, there are 13-1=12 movies to choose from so your option are a bit limited 12 ways.
For the 3rd you have 13-2=11
For the 4th there are 10
5th is 9
6th is 8
7th is 7

Answer 4

In maths as this are independent choices you have to multiply these together:
13*12*11*10*9*8*7

Answer 5

The only thing that we have to consider if we counted the same combination multiple times or not.
The answer is yes we have many many options that we considered multiple times. How is that?
Lets say you watch films ABCDEFG or GFEDCBA. All in all you saw the same 7 movies just in different order.

Answer 6

How many times did we count the same multiple times.
That is 7*6*5*4*3*2*1

Answer 7

Same logic as above for this.
So the final answer is:
13*12*11*10*9*8*7 divided by 7*6*5*4*3*2*1 = 1716

Answer 8

its starting to make a little more sense now, thanks

Answer 9

so would it be 8, 648, 640 or 4, 324, 320

Answer 10

@Andras

Answer 11

8, 648, 640 or 4, 324, 320 what are these numbers?

Answer 12

@Andras 8, 648, 640 and 4, 324, 320 are the choices..