Question

if anyone can help me with question i would really appreciate it

A signal is made by placing 3 flags one above the other, on a flag pole. If there are 7 different flags available, how many different possible signals can be flown?

Answer 1

it looks like order counts here

Answer 2

so we use n P r when we want to count how many ways to choose r elements from a set of n elements , when order counts

Answer 3

n P r = n! / ( n-r)!

Answer 4

order counts only in the fact that we need to determine in how many different ways, or how many different combinations these 7 flags can make when they are placed in the 3 positions o n the flagpole to create as many distinct signals as possible

Answer 5

as far as i can see, wouldnt it be 7*7*7 = 343

Answer 6

even though the question does not call for replacement?

Answer 7

7*6*5
There are 7 ways the first flag can be choosen,for each 7 ways there are 6 ways to choose the second flag,and for every 6 ways there are 5 ways to choose the third one.

Answer 8

OK, now that I've looked at that again, we are starting off with only 7 seven flags and are looking for the different possibilities which these 7 flags put in the 3 positions of the flag pole can make. So i guess it makes sense if you use one flag in one position, you would only have 6 remaining. Use another you have five remaining.

Answer 9

right

Answer 10

label the positions of the flag top, middle, bottom.
for the top flag you can pick 7 flags. once you pick a flag, you have 6 remaining flags to pick for the middle position.
and then you have 5 remaining flags to pick for the bottom positions

Answer 11

@barsanophius correct!