Number of combinations without repetition

Question

I have a database table that has 50 fields. what is the number of all unique combinations of the 50 fields I can use for filtering the data? for example I can use just field one. I can use fields 6 and 10 or any number of fields in my filter set.

Answer 1

Let r = the number of fields chosen. n = 50. If C(50,r) is the number of ways to choose r fields from 50, then you will need to SUM all of the C(50,r) for r = 1 to r = 50.

These C(n, r) numbers appear in "Pascal's triangle". n is the "row number" of the triangle and r is the position in the row.

If that is the case, then are you not interested in the 50th row? And if you are looking at "all values of r", then are you not interested in adding up all the numbers in the 50th row?

What is the sum of all numbers in the nth row of Pascal's triangle? _____

The sum of values in the nth row of Pascal's triangle is 2^n, by the way. [ ^ means exponent ]