Yes. The 1680 ways includes this sequence and all sequences in which C speaks before A, A before D, and D before F. One must understand that to cancel the arrangements among a particular set of people, DIVIDE the total arrangements possible by the number of arrangements of the members whose ORDER should be fixed. In case you are finding difficulty still understanding this question, take a smaller sample. lets say for 2 people A & B. If they were to arrange themselves where anyone could speak first, there would be 2! ways. Now if we say, only A speaks first then we have 2!/2! =1 way only.
Take 3 guys now. A, B & C.
Toatal ways of arrangement: 3! They are: ABC, ACB, BAC, BCA, CAB, CBA. Now we say A is before C. How many ways? 3!/2! = 2 ways. They are : ABC, BAC, ACB.
Take 4 now:
A, B, C, D. Total ways: 4!=24 They are:
ABCD, ABDC, ACBD, ACDB, ADBC, ADCB,
BACD, BADC, BCDA, BCAD, BDCA, BDAC,
CABD, CADB, CBAD, CBDA, CDAB, CDBA,
DABC, DACB, DBAC, DBCA, DCAB, DCBA.
Lets say A will always speak before B . How many ways? 4!/2!=12 They are:
ABCD, ABDC, ACBD, ACDB, ADBC, ADCB,
CABD, CADB, CDAB,
DABC, DACB, DCAB.
Lets say A will speak before B and B will speak before C. How many ways? 4!/3!=4 They are:
ABCD, ABDC, ADBC,
DABC.
Boy, I can't explain any further...need some water !!
But hope this helps !!
knight247 wrote:Ok here is where I have an issue. Does the 1680 ways include a sequence like the following
C B A E D F H. This is what I'm not quite able to follow. Hope someone can clarify this for me. Thanks
