Question

Explain the real-world meaning of the fact that 40C5 and 40C35 are equal to each other.

Answer 1

So I take you know mathematically why they are equal.

Now, why intuitively are they equal. 40C5 is the number of ways of choosing 5 things out of a collection of 40; so given the 40 things in front of you, pull 5 of them out.

On the other hand, 40C35 is the number of ways of choosing 35 things out of a collection of 40;

Well, choosing 35 things out of a collection of 40 is equivalent to deciding 5 things you don't pull out. And that is therefore the same thing as the number of ways of choosing 5 from 40.

Answer 2

you have a box with 40 balls in it....

1) how many ways to choose 5 from the box without replacement

2) how many ways can you choose 35 balls to keep in the box