Question

in a mountain climbing expedition5 men and 7 men are to walk single file so that no two men are adjacnet. how many ways are possible? PROBABILITY AND STATISTICS :)

Answer 1

Did you do any work already?

Answer 2

I think this is a question where permutations or combinations coem in, right?

Answer 3

YES PERMUTATION AND COMBINATION .

Answer 4

What's the different between the 2 again?

Answer 5

NOT WORKING YET ..STUDYING ..SO I NEED YOUR HELP .. I DONT KNOW HOW WILL I ANSWER THAT :)

Answer 6

It's that, subtracted by the possibility of any 2 men being adjacent. I think you have to do that manually.

Answer 7

help me how?

Answer 8

What's the difference between combinations and permutations?

Answer 9

frankly, with 12 men marching up a mountain single file, it is going to be impossible to find any ordering where you have "no two men adjacent"... Are you sure there aren't any women?

Answer 10

i THINK there is a totally of 7 men, but 2 out of 5 men are not to be adajacent.

Answer 11

i was guessing 7 women and 5 men no men adjacent.

Answer 12

yes ..it's 5men and 7 women ..

Answer 13

Oops. Worded your question wrong.

Answer 14

can you answer that please :((

Answer 15

I dunno. Im fuzzy on this.

Answer 16

I shouldnt be though.

Answer 17

you'll first need to commit to putting women in between, to create a line of M W M W M W M W M, to separate the 5 men. There are now 6 "bins" (places) in which to drop in 3 "identical objects" (the last 3 women): for example you could put all 3 additional women in front (www)MWMWMWMWM or spread them out in some way: (w)MW(w)MWMW(w)MWM.

You might know the right formula for 3 objects into 6 bins, or you might just count them by hand.

Answer 18

THATS IT? THANKS :))

Answer 19

There you go. Good work Fixer.

Answer 20

can i know the final answer?

Answer 21

(i) how many ways are there to put 1 red, 1 blue, and 1 green book onto 6 empty bookshelves?
(ii) how many ways are there to put 3 identical books onto 6 empty bookshelves? <- (3 women into 6 places in line)

equivalently,
(i) how many ways are there to put 1 red, 1 blue, and 1 green ball into 6 urns?
(ii) how many ways are there to put 3 identical balls into 6 empty urns?

You'll want to be able to know (or know where to look up) these formulas, or people will be working these problems for you til they're blue in the face.

I looked them up at
http://www.johndcook.com/TwelvefoldWay.pdf
and got for your problem:
\[\left(\begin{matrix}n+k-1 \\ k\end{matrix}\right) = \left(\begin{matrix}6+3-1 \\ 3\end{matrix}\right) = 56\]