patrol.
In how many ways can the twelve officers be divided into three teams of 4 officers and each team be assigned the same duty in a given week?
更新1:
A) 1/2 ( 12 ) 4 4 4 B)(4!)^3 C) ( 12 ) 4 4 4 D)3! ( 12 ) 4 4 4 E) 1/3! ( 12 ) 4 4 4
Finite Question
2014-10-15 5:37 pm
Every week, twelve officers in a large police force are divided into teams and each team is assigned one of three kinds of duties for the week: surveillance, security or
patrol.
In how many ways can the twelve officers be divided into three teams of 4 officers and each team be assigned the same duty in a given week?
patrol.
In how many ways can the twelve officers be divided into three teams of 4 officers and each team be assigned the same duty in a given week?
回答 (2)
2014-10-15 5:50 pm
✔ 最佳答案
Answer:12!/(4! * 4! * 4!)
= 479001600/(24 * 24 * 24)
= 34650
Explanation 1:
Out of 12 officers, choose 4 from them to be assigned to Task 1.
The number is 12C4.
In the remaining 12 - 4 = 8 officers, choose 4 from them to be assigned to Task 2.
The number is 8C4.
For the final remaining 8 - 4 = 4 officers, choose all 4 to be assigned to Task 3.
The number is 4C4.
The total number of ways is
12C4 * 8C4 * 4C4
= 12!/(4! * 8!) * 8!/(4! * 4!) * 4!/(4! * 0!)
= 12!/(4! * 4! * 4!)
Explanation 2:
Consider the permutation of 12 officers in a row.
There are 12! of ways.
Assign the first 4 to do Task 1, the next 4 to do Task 2, the last 4 to do Task 3.
Then, the arrangements within the first 4 do not affect the overall assignment, thus the above number needs to be divided by 4!.
Similarly, for the middle 4 and the final 4, the total number needs to be divided by 4! for each group.
Thus, the total number of ways is
= 12!/(4! * 4! * 4!)
2014-10-15 18:00:43 補充：
答案是 C.
［ １２ ］
［４，４，４］ ＝ １２！／（４！４！４！）
2015-10-16 11:24 pm
the answer is A not C
收錄日期: 2021-04-23 23:48:57
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