这几个词意思大致相同，都有允许，准许的意思。稍有区别如下：
permit 1、允许，准许=allow, 但permit 稍稍正式一些，常指上级对下级的允许，许可
Do you permit/allow your children to smoke? 你允许孩子们抽烟吗？
She won't permit/allow dogs in the house. 她不允许屋里有狗。
2、允许，容许
If my health permits, I will go hiking with you next year. 如果身体允许明年我和你一起去远足。
allow 普通意义上的 “允许，准许”， 使得以发生
Smoking is not allowed in public place. 在公共场所不允许抽烟。
My mother doesn't allow me to watch TV before I finish my homework. 我完成作业之前我妈妈不允许我看电视。
This money allows me to buy a car. 这笔钱可使我买一辆汽车。
admit 常指不情愿地“承认，供认”; 准许进入; 容纳
He will never admit that he is wrong. 他从来不会承认他错了。
She admitted that she broke the cup. 她承认她打碎了杯子。
The ticket admits two people to the football match. 这张票准许两人入场看足球比赛。
The cinema admits about 100 people. 这个电影院可容纳大约100人。
approve 常指对文件，计划等的正式“批准，许可，认可”
The manager approved my proposal. 经理批准了我的建议。
The budget plan was approved. 预算计划被批准了。
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