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March 2nd, 2016, 01:51 PM   #1
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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,


Last edited by mat; March 2nd, 2016 at 01:55 PM.
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March 2nd, 2016, 04:56 PM   #2
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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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