How many different combinations of pennies nickles dimes and

How many different combinations of pennies, nickles, dimes and quarters can a piggy bank contain if it has 40 coins in it?

Solution

How many different combinations of pennies, nickles, dimes and quarters can a piggy bank contain if it has 40 coins in it?

The number is the same as the number of nonnegative integer solutions to the

Equation p+n+d+q=40

The answer is (40+4-1) C (4-1) = 43C3   = 12341