64. In how many ways can 3 identical books be distributed among twelve schoolchildren if no more than one book can be given to any one child?
64. If the books were different, the number of ways to distribute them among twelve schoolchildren would be 12.11 * ... * 10 = 1320. Let's choose any three schoolchildren. If, having three different books, we distribute them, giving one to each of these schoolchildren, it will be found that there are 6 ways to distribute the books. Under the same conditions, three identical books can be distributed in only one way. And this will be the case for any three schoolchildren. Therefore, the number of ways to distribute three identical books among 12 schoolchildren will be 3! times less than if the books were different. Finally, we get $12 \cdot 11 \cdot 10: 3!=220$ ways.