permutation Q's (1 Viewer)

[5647382910]

1) In how many ways can 4 people be accomodated if there are 4 rooms available answer: 256
2) In how many ways can 8 oarsmen be seated in an eight oared boat if 3 can row only on the stroke side and 3 can row only on the bow side? answer: 1152

thanks in advance

 

[Pwnage101]

1) 4^4, as the first person has 4 choices, the 2nd has 4 choices, the 3rd has 4 choices and the 4th hs 4 choices, ie 4 x 4 x 4 x 4 = 4^4 = 256

2)1152 ok lets assume there are 4 on each side. There are 3 ppl who have to go onn the right side - to chose where these 3 positions will be out of the 4 possible, it is 4C3. These 3 ppl have 3! ways of sitting in these seats, so there are 4C3 X 3! of seating those 3 ppl. Same for the people on the left. Then, there are 2 ppl remaining, and can be seeated in 2! (=2) ways

so it is 4C3 x 3! x 4C3 x 3! x2! = 1152

 

[jet]

Question 2:
the first person to row on the bow side has 4 choices, the second 3 and the third 2.
this occurs on the other side aswell.
The remaining two can row on either side. This gives 2 choices.
Answer = 4 x 3 x 2 x 4 x 3 x 2 x 2
= (24)^2 x 2
=1152.

 

[5647382910]

Thanks heaps guys

 

[lyounamu]

Ah, I just love perm and comb. It requires the least amount of working out and quick.

 

[dp624]

Ah, I just love perm and comb. It requires the least amount of working out and quick.

lolwut i hate P&C. it was the only legitimate (ie non silly) mistake i lost in the 4u external haha
its so annoying!

 

[lyounamu]

lolwut i hate P&C. it was the only legitimate (ie non silly) mistake i lost in the 4u external haha
its so annoying!

Yeah, some questions are pretty annoying.

But I just love it purely for the reason that it basically requires least working out... (except some really easy complex questions)

 

[5647382910]

well, i absolutely hate em,
stuck on another q,
In how many things can n things be shared between two people?
im gettin 2^n - 1 - n but its 2^n - 2
thanks in advance

 

[independantz]

well, i absolutely hate em,
stuck on another q,
In how many things can n things be shared between two people?
im gettin 2^n - 1 - n but its 2^n - 2
thanks in advance

Consider:
n=1, can't be shared
n=2, 2 ways
n=3, 6 ways
n=4, 14 ways
....
n=n, 2^n-2 ways

 

[5647382910]

Consider:
n=1, can't be shared
n=2, 2 ways
n=3, 6 ways
n=4, 14 ways
....
n=n, 2^n-2 ways

isnt there a way of reasoning why?
like for at least 1 object you can reason that every object can be dealt with in two (it can be included or rejected) ways therefore you can deal with all the objects taking any at a time 2^n ways; but considering rejecting all objects as an unwanted possibility; 2^n - 1 times. But for at least two objects, i cant see how we get 2^n - 2; i see it as we subttract the one case when all are rejected (subtracting 1), and, taking 1 object at a time, this can be done n ways so we suntract n. Therefore were left with 2^n - 1 - n for all the possibilities of at least two objects.
maybe ive misinterpreted the question.... if I have can someone show me why and if my answer is correct for taking taking n objects at least 2 at a time

 

[lolokay]

"In how many ways can n things be shared between two people?"

Each of the n objects can be given to one of 2 people (2ⁿ ways) but neither of the 2 can recieve every thing (-2 of the ways)

 

[kurt.physics]

That's from Couchman right? Those questions look familiar.

I know the boat one is from Cambridge Extension 1.

 

[5647382910]

"In how many ways can n things be shared between two people?"

Each of the n objects can be given to one of 2 people (2ⁿ ways) but neither of the 2 can recieve every thing (-2 of the ways)

ohh crap..... i guess i thought too much
thanks for pointing that out for me

 

[Timothy.Siu]

I know the boat one is from Cambridge Extension 1.

its definitely in fitzpatrick

 

[lyounamu]

its definitely in fitzpatrick

Yep, it is.

 

[kurt.physics]

Yep, it is.

oh yeh, but its funny; Cambridge has an almost exactly the same question! (Cam Green Ex10E Q22).