2013 HSC Examination M/C Q.10 (1 Viewer)

[Aquallis]

What is the logic behind solving question 10 (m/c) of the 2013 HSC paper? It goes like this:

A hostel has four vacant rooms. Each room can accommodate a maximum of four people. In how many different ways can six people be accommodated in the four rooms?

A) 4020
B) 4068
C) 4080
D) 4096

 

[aDimitri]

total ways - ways with 6 people in one room - ways with 5 people in one room

 

[Aquallis]

What would be the mathematical expression for this? I misworded my question haha - I meant logic as in the mathematical process in which the answer is achieved

 

[aDimitri]

total ways is 4^6
ways with 6 in one room is 4C1
ways with 5 in one room is 6C1*4C2*2

 

[Elise8842]

Each room can have max four people


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[Elise8842]

So how can there be 5 in one room?


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[Aquallis]

Ok thanks!

 

[Elise8842]

Oh sorry didn't read properly


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