Question

Explain verbally why n choose x is the same as n choose (n-x).

I showed why they are the same mathematically, but I am not sure how to word it. Thanks.

Answer 1

One interesting way would be to show it in Pascal's triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
....

notice that in any row, entries equidistant from either the left or the right are equal.
in my last row, the 28 is the 3rd from the left and the 3rd last at the right.
in row n, x and n-x are equidistant from left or right.

Answer 2

I understand the figure but I don't understand how I should word it to make it relevant to statistics