Question

Ana has one coin of 5 cents, one coin of 10 cents, one coin of 20 cents and one coin of 50 cents. how many different values can she make with these coins?

Answer 1

Ana has 4 coins with different values(5, 10, 20, 50) and you are asked to find how many different sums they can make.  You can see every value as a separate combination and multiply it.
There is 1 coin for every value and it can be either used or not used, so there are two probabilities for each coin value. The calculation would be:
C(2,1)= 2!/1!= 2

There are 4 values of coins, so the total probability would be:
4 * C(2,1)= 4*2=8 ways