+328 Mable has a penny, a nickel, a dime, and a quarter (1, 5, 10, and 25 cents, respectively).How many different amounts can Mable make using at least one of the coins she has?
+128475 C(4,1) = 1 , 5 , 10 , 25 cents
C(4,2) = ( 1 + 5) (1 + 10) (1 + 25) ( 5 + 10) ( 5 + 25) (10 + 25) =
6 11 26 15 30 35 cents
C(4,3) ( 1 + 5 + 10) (1 + 5 + 25) (1 +10 + 25) ( 5 + 10 + 25)
16 31 36 40 cents
C( 4, 4) = ( 1 + 5 + 10 + 25) = 41 cents
So 15 different amounts
Note that this is the sum of the entries on Row 4 of Pascal's Triangle - 1 = 2^4 - 1 = 15
