Kenneth Rosen Edition 7 Exercise 6.5 Question 12 (Page No. 432)

Question

How many different combinations of pennies, nickels, dimes, quarters, and half dollars can a piggy bank contain if it has $20$ coins in it?

Answer 1

First let's define a few variables:

Let,

X1,X2,X3,X4,X5=Number of pennies, nickels, dimes, quarters and half-quarters in the piggy bank.

Then we have that

X1+X2+X3+X4+X5=20 whereXi≥0 ,1<=i<=6

The number of solutions 

C(20+5−1,20)

=C(24,20)

=10626

Hence we have 10,626 such combinations.