6 different pigeons are assigned to live in six different pigeon holes.
In how many ways can any three of them be placed in the wrong pigeons holes?
Permutation & Combination
2015-01-02 12:08 am
回答 (3)
2015-01-02 1:37 am
✔ 最佳答案
Assume A, B, C placed in wrong pigeon holes,ie, B - C - A, or C - A - B
so there are 2 different ways.
As there are C(6,3) ways for 3 different pigeons, so altogether, there are :
2 * C(6,3)
= 40 (ways)
2015-01-01 18:39:35 補充：
例如A, B, C坐錯位，有兩種錯法：
B坐A位，C坐B位，A坐C位；
或者
C坐A位，A坐B位，B坐C位。
6選3人有 C(6,3) 選擇，每種選擇有兩種坐位錯法，
所以共有40種。
2015-01-01 22:38:15 補充：
You are welcome.
2015-01-02 9:15 am
呢個係 derangement 的問題。
先選 3 隻對(或錯)的鴿：6C3 = 20 個情況。
然後處理錯排的情況：
３個物件的錯排數是 !3 = 2
先選 3 隻對(或錯)的鴿：6C3 = 20 個情況。
然後處理錯排的情況：
３個物件的錯排數是 !3 = 2
2015-01-02 1:49 am
Assume A, B, C placed in wrong pigeon holes,
ie, B - C - A, or C - A - B
so there are 2 different ways.
As there are C(6,3) ways for 3 different pigeons, so altogether, there are :
2 * C(6,3)
= 40 (ways)
唔明白點解要X2
2015-01-01 19:30:43 補充：
完全明白了，THANK YOU
ie, B - C - A, or C - A - B
so there are 2 different ways.
As there are C(6,3) ways for 3 different pigeons, so altogether, there are :
2 * C(6,3)
= 40 (ways)
唔明白點解要X2
2015-01-01 19:30:43 補充：
完全明白了，THANK YOU
收錄日期: 2021-04-18 14:39:34
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