2008 HSC Q4b (1 Viewer)

[gr_111]

2008 HSC Q4b

Barbara and John and six other people go through a doorway one at a time.

(i)In how many ways can the eight people go through the doorway if John goes through the doorway after Barbara with no-one in between?

Is the answer to this ??? My reasoning is that there are eight people but John and Barbara must go together so there are seven 'units' to arrange. But John must be after Barbara, so you halve the number of ways of arranging the seven units. Right or wrong?

 

[D94]

There's no need to halve the 7!. If John goes through after Barbara, the total number of ways they can go through is 1!, or simply, 1 way. You consider that as one unit, then along with the other 6, that's 7 units, so that can be arranged 7! ways, then you multiply by how many ways the combined unit can be arranged, which is just 1, so it should just be 7!.

 

[gr_111]

yep, i see it now, thanks.

 

[shongaponga]

Wrong.
As you said, Barbara and John will have to remain together, with John always behind .'. Once they have gone through the doorway, there are only 7 units left to arrange. So 7! ways = 5040

 

[shongaponga]

D94 beat me to it lol.