If the class contains 7 mechanical, 6 civil and 5 electrical and we require that the 9 individuals who give their presentations on day 1 must include 3 mechanical, 3 civil and 3 electrical, how many different orders of presentation are there for day 1?
The Attempt at a Solution
It looks like we have to combine 3 permutations together, taking only 3 students from each group.
I have no clue how to do this, I have tried reducing the problem to :
2 mechanical, 2 civil and 2 electrical and 1 per group must give a presentation.
I computed by hand the different orders of presentation, but then I don't know what formula to use to arrive at the same answer.
So If we have :
Mechanical students : A, B
Civil : C, D
Electrical : E, F
Then the different presentations on day 1 would be :
A, C, E
A, C, F
A, D, E
A, D, F
B, C, E
B, C, F
B, D, E
B, D, F
8*2*3 = 48 possible presentation order in this simple case, am I right?