Chapter 9, Counting and Probability - Section 9.1 - Counting - 9.1 Exercises - Page 658: 55

277200

We can use the general idea that we can order these coins, if they were distinguishable, in $12!$ ways. However, since they are indistinguishable, we can swap around the types of coins, so we divide by $4!*3!*2!*3!$ accounting for the pennies, nickels, dimes, and quarters respectively. $$\frac{12!}{4!*3!*2!*3!}=\boxed{277200}$$