Name: 【TED-Ed】一副牌可以有幾種排列方式？- 亞內-卡伊金 (【TED-Ed】How many ways can you arrange a deck of cards? - Yannay Khaikin)
Uploaded: 2021-01-14T04:58:57.000Z
Duration: 3 min 42 s

祈使句型

挑選一張牌，任何一張都可以。

Actually, just pick up all of them and take a look.

事實上，只需將所有牌拿起來看看，

This standard 52-card deck has been used for centuries.

這標準的 52 張卡片已經使用了好幾個世紀。

are shuffled in casinos all over the world,

And yet, every time you pick up a well-shuffled deck

that has never before existed in all of history.

The answer lies in how many different arrangements

of 52 cards, or any objects, are possible.

或是其他東西的排列方式可能有多少種。

Now, 52 may not seem like such a high number,

現在，52 看起來似乎不是很大的數字，

but let's start with an even smaller one.

那我們從較小的數字開始說起。

To start off, any of the four people can sit

最後一個站著的人沒有選擇權，

If we manually write out all the possible arrangements,

如果我們手寫列出所有可能的組合，

that four people can be seated into four chairs,

所以我們看看是否有更快的方法。

you can see that each of the four initial choices

leads to three more possible choices for the second chair,

導致第二張椅子只有三個人可以選擇坐上去，

第三張椅子只有兩個人可以選擇坐上去。

So instead of counting each final scenario individually,

我們可以將每張椅子的可被選擇的機會相乘，

we can multiply the number of choices for each chair:

We start with the number of objects we're arranging,

我們從排列的對象數開始排列，

and multiply it by consecutively smaller integers

So exciting that mathematicians have chosen

As a general rule, the factorial of any positive integer

與所有較小的整數，直到 1 的乘積。

Fortunately, we don't have to calculate this by hand.

Just enter the function into a calculator,

when the Big Bang is thought to have occurred,

the writing would still be continuing today

ways to arrange this simple deck of cards

So the next time it's your turn to shuffle,