prelim probability question (1 Viewer)

[shady145]

There are 16 cards. 4 blue, 4 red, 4 green, 4 yellow. the cards in each coloured set are number 1 to 4. how many arrangements (in a stright line) are possible if all the same coloured cards have to be next to each other. eg. all blue then then all red then all green then all yellow.

thnx

 

[gurmies]

Have you got the answer?

 

[shady145]

no. it was in my test, i got it wrong, the teacher was explaining the answer but he decided he better have another look coz he cant give reasons for what he did, so i was wondering if i was maybe right. i got, (4!)^5=7962624

 

[gurmies]

lol, I got the exact same answer. 4!.4!.4!.4! = (4!)^4 to arrange all of them in their colours, then 4! to arrange the coloured groups amongst eachother = (4!)^5...answer is a tad too big ?

 

[khorne]

Well, how many ways of arranging the cards? there's 4! ways, so 24 ways. Again, in each set of cards, there's 4! ways of arranging the numbers, so yes 24^5 or 4!^5...Personally, I think there's another condition.

 

[grasshopper1]

4!x16???

 

[shady145]

to gurmies. it seems correct to me, but my teacher had something like 142 as the answer. but he said he is going over it again since he cant reason with his answer. having a look, there are 16! ways of ordering all the cards so maybe (4!)^5 is correct

 

[Timothy.Siu]

was that the exact question?

 

[addikaye03]

-Each set of four can be arranged in 4! .'. 4! x 4! x 4! x 4!
-These four sets can be arranged in different orders, the first set has 4 different positions available initially, the following set has 3 spots to choose from and so on so 4!

So i would think the answer would be (4!)^5

 

[khorne]

They're not the same, they have numbers on them

 

[shady145]

was that the exact question?

no not the exact question, not word for word. i dnt have the question but i read it enought times to remember the majority of it. but i can see one word i missed. the question says how many distinct arrangements are possible, not just how many arrangements are possible

 

[khorne]

4!x4!/4 = 144 that sounds like the answer your teacher had.

 

[shady145]

4!x4!/4 = 144 that sounds like the answer your teacher had.

no, he showed me his workign once, and he said, y do i have a 2 in there. he had 2x?x?=100sumthing

 

[khorne]

Incompetent maths teacher...If the teacher can't do the test, there's something wrong.

 

[shady145]

nah he is a good teacher