• Best of luck to the class of 2024 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • YOU can help the next generation of students in the community!
    Share your trial papers and notes on our Notes & Resources page

perms and combs (1 Viewer)

eternallyboreduser

Well-Known Member
Joined
Jul 4, 2023
Messages
564
Gender
Undisclosed
HSC
N/A
Why are the answers 40320, 20160 and 17280?

I did this:
a)8c4×4!×4c4×4!/2!=20160
b)1×7c3×4c4×4!×4!/2!=10080
c)1×7c2×4c4×4!×4!/2!=6048

8 ppl are to form 2 queues of 4, in how many ways can this be done if:
a)no restrictions
b)jim only stands in left queue
c)sean and liam must stand in the same queue
 

cossine

Well-Known Member
Joined
Jul 24, 2020
Messages
631
Gender
Male
HSC
2017
Why are the answers 40320, 20160 and 17280?

I did this:
a)8c4×4!×4c4×4!/2!=20160
b)1×7c3×4c4×4!×4!/2!=10080
c)1×7c2×4c4×4!×4!/2!=6048

8 ppl are to form 2 queues of 4, in how many ways can this be done if:
a)no restrictions
b)jim only stands in left queue
c)sean and liam must stand in the same queue
a) is very easy. Notice 8! = 40320.
 

liamkk112

Well-Known Member
Joined
Mar 26, 2022
Messages
1,037
Gender
Female
HSC
2023
Why are the answers 40320, 20160 and 17280?

I did this:
a)8c4×4!×4c4×4!/2!=20160
b)1×7c3×4c4×4!×4!/2!=10080
c)1×7c2×4c4×4!×4!/2!=6048

8 ppl are to form 2 queues of 4, in how many ways can this be done if:
a)no restrictions
b)jim only stands in left queue
c)sean and liam must stand in the same queue
for a and b, no need to divide by 2!, otherwise your reasoning seems correct judging from the numbers you’ve used.

for c) you have two cases; they’re both in the first queue and they’re both in the second queue. now there are 2 ways to choose which queue they’re both in, and 6C2 ways to pick two more people to go into the queue with them both, and 4! ways to organise that queue. there are then 4C4 x4! ways to do the other queue, which gives a total of 2x6C2x4!x4C4x4!= 17280 ways
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top