This is a combination problem, where we want to choose 4 members from a total of 20 members. The formula for combinations is:
n C r = n! / (r!(n-r)!)
where n is the total number of objects, and r is the number of objects we want to choose.
Plugging in the values,
20 C 4 = 20! / (4!16!)
We can simplify this expression by canceling out the common factor of 4! in both numerator and denominator:
20 C 4 = (20 x 19 x 18 x 17) / (4 x 3 x 2 x 1)
20 C 4 = 4845
Therefore, there are 4845 different combinations of four members that can be chosen from a school club with 20 members.