Question: 1. Find a generating function for the number of ways we can make change using dimes, quarters and half dollars. What is the largest amount

1. Find a generating function for the number of ways we can make change using dimes, quarters and half dollars. What is the largest amount (in cents) under a dollar which we can make change for (using these denominations) in only one way.

2. A bakery sells salted pineapple rolls in bags of three, five, and twelve. If there are four bags of three, four bags of five, and three bags of twelve left available, find a generating function for the number of ways we can purchase k rolls. What is the largest number of rolls we can order in exactly three different ways?

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