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[azureus88]

need help with 2 problems:

1) "in how many ways can 4 people be accommodated if there are 4 rooms available" [ans 256]

and...

2) "in how many ways can 8 oarsmen be seated in an eight-oared boat if 3 can row only on the stroke and 3 can row only on the bow side" [ans 1152]

For question 1, i got 244 if the following working which is off by a bit:

1person per room and 4 rooms occupied = 4!
4 people/1 room occupied = 4
2 people/2 rooms occupied = <SUP>4</SUP>C<SUB>2 </SUB> x 4 x 3
2 people/3 rooms occupied = <SUP>4</SUP>C<SUB>2 </SUB> x 4 x 3 x 2

 

[Trebla]

The first one is just 4⁴.
Each person can occupy one of four rooms so there are 4 ways for one person.
There are four people so its 4 x 4 x 4 x 4 = 256.

 

[Timothy.Siu]

well for the 2nd one, okay so i pretended that the guys that can go on both sides were on one side, so then it would be 4!x4! but those 2 guys can swap places so therefore its 4!x4!x2