數統科，請打救我－yffuhxy的部落格

標題:

數統科，請打救我

發問:

七個國家的總理A、B、C、D、E、F和G在一個高峰會議上演講。 (a)求下列各情況之排列總數 (i) A在C之前演講。 (ii) A在C之前，且C在E之前演講。 (b)在(a)(ii)排列中，C緊隨A之後演講的方法有多少種?

最佳解答:

This is a 'not so obvious' question! I will try my best to explain (a)(i) I am going to use a 'short cut' method for this one. First let's consider a question: which of the following have higher chance to speak first? A or C? Since THERE IS ABSOLUTELY NO FURTHER INFORMATION ON THAT, we can say A and C have EQUAL chance to speak before the other one! So total number of ordering which have A speak before C = total number for ordering those 7 people / 2 = 7! / 2 = 5040 / 2 = 2520 (a)(ii) Suppose 1, 2, 3 ... 7 are the order of speaking (Step 1) First, we have to assign numbers to A, C and E How many ways can A, C, E be assigned? This question is the same as asking "in how many ways can we pick 3 numbers out of 7 numbers" Answer = 7C3 ============================================== Note that the answer is NOT 7P3? Since, according to the question, A