My Math Forum Permutation with a Condition

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 March 2nd, 2016, 01:51 PM #1 Newbie   Joined: Mar 2016 From: California Posts: 1 Thanks: 0 Permutation with a Condition I apologize if this is in the wrong section of the forum, or if this is not phrased using the proper terminology--I am not a mathematician. Suppose there is a case, wherein a personal assistant must schedule seven appointments with five different individuals, with one individual "A" having three appointments. So, it looks like this: AAABCDE for a total of seven appointments. Now, let's suppose there is a condition that stipulates A's three appointments cannot be scheduled consecutively, so a combination like AABACDE cannot occur because it violates that condition. Is there anyway for me to know the total number of possible scenarios (arrangements of ABCADAE where A does not appear consecutively) without writing out all the possible conditions one at a time until the list of possible scenarios has been exhausted? Much thanks, Mat Last edited by mat; March 2nd, 2016 at 01:55 PM.
 March 2nd, 2016, 04:56 PM #2 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 Find (H) the number of all the possible positions A may have (1,3,5),(1,3,6), etc. There are 4! = 24 possible permutations for the other 4 appointments, so you final answer is 24H.

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