首先看一下两者的区别：
no one
1.表示没有人,
2.作主语时,谓语动词用单数 No one is over there.
3. 回答who 问句：Who is in the room? No one.
none
1.全部否定,表示没有东西/人
2.作主语时,如果指人,谓语用复数；如果指物用单数.
None of the boys like singing.
None of the books belongs to him.
从句子意思可知,but后面是表否定的,应用none,指代前面提到的all his realatives ,是复数形式