SOLUTION: Hello Sir! My email address is: shahnirav72@gmail.com. Question is as follows: Seven different lecturers are to deliver lectures in seven periods of a

Algebra ->  Permutations -> SOLUTION: Hello Sir! My email address is: shahnirav72@gmail.com. Question is as follows: Seven different lecturers are to deliver lectures in seven periods of a      Log On


   

Question 1063162: Hello Sir! My email address is: shahnirav72@gmail.com.
Question is as follows: Seven different lecturers are to deliver lectures in seven periods of a class on a particular day. A,B and C are 3 of the lecturers. The number of ways in which routine can be prepared such that A delievers his lecture before B and B before C is? Options are (a) 420 (b) 120 (c) 210 (d) 840 Please help me out to solve this sum. Thanks a lot.......... I have tried much by 5P5*5P5*5P5= 5*5*5=125 but that doesn't match the answer.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We need to reserve 3 slots for A, B, and C.
There are 7%2A6%2A5%2F%282%2A3%29=7%2A5=35 sets of 3 schedule slots
that we can reserve for professors A, B, and C.
The remaiming 7-3=4 slots will be filled by the other e lecturers in any order.
There are 4%21=4%2A3%2A2=24 possible permutations
indicating the order of those lecturers' presentations.
Combining those choices there are
35%2A24=highlight%28840%29 schedules for the 7 lectures
that meet the requirement of having A before B, and B before C.
Without that requirement, there would be
7%21=7%2A6%2A5%2A4%2A3%2A2=5040 possible schedules.