permutation

niharika_kumar · 2014-03-31 19:13:42

Q.) There are stall for 10 animals in a ship.In how many ways can the ship load be made if there are cows ,calves and horses to be transported, animals of each kind being not less than 10?

Last edited by niharika_kumar (2014-03-31 19:59:25)

bobbym · 2014-03-31 19:56:11

Is there something missing in that space between transported and animals?

niharika_kumar · 2014-03-31 19:59:57

sorry, that was a mistake.I corrected it.

bobbym · 2014-03-31 20:03:35

Hi;

Is that the exact wording of the problem?

niharika_kumar · 2014-03-31 20:10:12

yes and i find it difficult to understand.
the answer in the book is given as 3^10.

bobbym · 2014-03-31 20:14:03

There wording is a little funny but there are 3 for the first stall and 3 for the second and 3 for the third... 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 3^10.

niharika_kumar · 2014-03-31 20:18:22

i still don't get this.

bobbym · 2014-03-31 20:29:03

Here is one permutation of the stalls:

{cow, cow, calf, horse, cow, horse, horse, calf, calf, cow}

here is another

{horse, cow, calf, cow, cow, cow, cow, horse, calf, cow}

and another

{cow, cow, horse, calf, horse, calf, calf, cow, cow, calf}.

Do you see that each stall has 3 choices, a cow or a horse or a calf?

niharika_kumar · 2014-04-01 16:57:25

so it was all about this.
"animals of each kind being not less than 10" <---what was the use of this sentence then

Agnishom · 2014-04-01 17:04:58

Since the title is 'permutation', I am assuming that the order matters.

For Each stall , you can do it in 3 ways (i.e, one of cows or calves or horses)

For 10 stalls, you can do it in 3^10 Ways

Agnishom · 2014-04-01 17:09:58

niharika_kumar wrote:

so it was all about this.
"animals of each kind being not less than 10" <---what was the use of this sentence then

I do not know but who cares?

niharika_kumar · 2014-04-01 17:17:27

hmmm, this sentence confused me.

thanks.

Agnishom · 2014-04-01 17:30:30

It means that the pool from which you are choosing animals has atleast 10 of each of those animals

bobbym · 2014-04-01 20:32:37

hmmm, this sentence confused me.

Confused me too.

eigenguy · 2014-04-02 13:02:56

I believe the intent is:
The ship can be loaded with 10 animals.
Animals available to be loaded consist of three types: Cows, calves, horses.
There are enough of each type of animal available to fill all 10 stalls with cows, or all 10 with calves, or all 10 with horses, if you desired.
Individual cows are not distinguishable from each other (so exchanging one cow for another does not constitute a different loading). The same is true of calves, and of horses.
However, and I base this only on the answer provided, not something that made it clear in the problem, the individual stalls are distinguished (so having a cow in #1 and a horse in #2 is a different loading from having a horse in #1 and a cow in #2, even if all the other stalls are the same).

Based on that understanding, the type of animal in each stall is independent from the types in the other stalls, and there are exactly 3 ways to fill each stall, so the total number of loadings is 3*3*3*...*3 = 3^10.

niharika_kumar · 2014-04-03 17:03:11

it makes it much clearer.

Math Is Fun Forum

#1 2014-03-31 19:13:42

permutation

#2 2014-03-31 19:56:11

Re: permutation

#3 2014-03-31 19:59:57

Re: permutation

#4 2014-03-31 20:03:35

Re: permutation

#5 2014-03-31 20:10:12

Re: permutation

#6 2014-03-31 20:14:03

Re: permutation

#7 2014-03-31 20:18:22

Re: permutation

#8 2014-03-31 20:29:03

Re: permutation

#9 2014-04-01 16:57:25

Re: permutation

#10 2014-04-01 17:04:58

Re: permutation

#11 2014-04-01 17:09:58

Re: permutation

#12 2014-04-01 17:17:27

Re: permutation

#13 2014-04-01 17:30:30

Re: permutation

#14 2014-04-01 20:32:37

Re: permutation

#15 2014-04-02 13:02:56

Re: permutation

#16 2014-04-03 17:03:11

Re: permutation

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