[中學] 黑板上排列與組合,你捨得解開嗎?

[playmypig (玩我豬)]

因為和書本上的答案有不同,所以想請教一下步驟:

題目:

Peter and 8 of his friends are divided into 3 groups for preparing a
christmas party. 1 of them decorated a christmas tree, 4 of them prepare the
christmas dinner and the remaining 4 go to buy christmas presents.

(1) Find the number of ways of forming the groups.
(2) If peter does not decorates the christmas tree and 2 particular friends must
be in the same group, find the number of ways of forming the groups.

答案:

(1) 630 (2) 120

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推 wayn2008    :1.(1,4,4):C(9,1)*C(8,4)*C(4,4)
→ wayn2008    :peter先選:2種 再用全部的情況(1,4,3)-那兩個再一起
→ wayn2008    :2*[C(8,1)*C(7,3)*C(4,4)-C(6,1)*C(5,1)*C(4,4)-
→ wayn2008    :C(6,1)*C(5,3)*C(2,2)]
→ wayn2008    :不...我看錯了...就把後面扣掉的加起來就是答案了
→ wayn2008    :一個是那兩個跟peter一組,一個是另外一組
→ playmypig   :你是計到120吧?但我不太明白你的式子喔
→ wayn2008    :我覺得第二題答案似乎怪怪的
→ wayn2008    :peter有兩種地方可去 WLOG 可以假設他去準備晚餐
→ wayn2008    :所以那兩個不是準備晚餐就是買禮物
→ wayn2008    :(1,1,4)那兩個準備晚餐  (1,3,2)那兩個買禮物
→ wayn2008    :我算出來似乎是180種耶= ="
→ wayn2008    :第二行之後都是第二題的
→ playmypig   :那應該是了,謝謝
→ sneak       : 不...我看錯了... https://noxiv.com
→ sneak       : 你是計到120吧?但我 https://daxiv.com