位
wèi
The counter that seats a person before it counts them: 位
The picture A place kept empty for someone, and an open palm pointing at that place while counting the people. 位 counts one person with a place laid out for them; 个 counts one of anything, asking neither shape nor standing.
Where the picture shows up in 位
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how many at the door
请问几位？
qǐngwèn jǐ wèi
How many in your party?
At the restaurant entrance a host opens a palm toward the empty table while asking the number.
几个人 to a customer sounds blunt.
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pointing with a place, not a finger
这位先生找您。
zhè wèi xiānsheng zhǎo nín
This gentleman is asking for you.
An upturned palm held toward the man standing by the counter as you speak.
这个人 is rough; 这位 is polite.
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raising everyone at once
各位请坐。
gèwèi qǐng zuò
Everyone, please be seated.
A hand sweeping open toward the whole room, offering the chairs.
各位 counts no one; it honours everybody present.
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people whose names go on a door
我们科有三位医生。
wǒmen kē yǒu sān wèi yīshēng
Our department has three doctors.
Tapping along three nameplates hanging side by side on clinic doors.
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one place in an order
她是公司第一位女经理。
tā shì gōngsī dì-yī wèi nǚ jīnglǐ
She is the company's first female manager.
A name being written onto the very top line of a list for the first time.
All of it in one picture
'How many of you' at the door is 位, 'this gentleman' beside the counter is 位, and 'everyone here' is 位 too. Three doctors with nameplates on their doors are counted with 位, and so is the first person to reach the top of a list. 位 lays out a seat for the person before it ever says a number, so the counting itself becomes courtesy. That is why guests, doctors and teachers take 位 and not 个.