✔ 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！）
