Determine the generating function for the number of ways to distribute 35 pennies (from an unlimited supply)

Question:

Determine the generating function for the number of ways to distribute 35 pennies (from an unlimited supply) among five children if (a) there are no restrictions; (b) each child gets at least 1₵; (c) each child gets at least 20₵ (d) the oldest child gets at least 10₵; and (e) the two youngest children must each get at least 10₵.