The German club has 12 members. In how many different ways can a subset of 6 members be selected to go on a field trip?

Question

The German club has 12 members. In how many different ways can a subset of 6 members be selected to go on a field trip?

Answer 1

This is a combinations problem ₁₂C₆ if you have a calculator you can plug it in, if you need to use the formula, this is the following:

12!/(6!(12-6)!)=12*11*10*9*8*7*6!/(6!*6*5*4*3*2) (the six factorials cancel, now let's cancel a few other values)

12*11*10*9*8*7/(4*3*5*2*6) (4 * 3 is 12 and 5 * 2 is 10 so we can cancel those out)

11*9*8*7/(3*2) (3 goes into 9 3 times and 2 goes into 8 4 times)

11*3*4*7=924 ways