Probability question?

Question

How many signals can be given by 5 flags of different colours, using 3 flags at a time?

ok.. 60 is the answer in my book, but i don't know how to get it.
Please explain the solution?

Answer 1

Order makes a difference when using signal flags (same as it does when using dots and dashes in Morse Code!)

Thus you are talking about permutations, not combinations.

5!/2! =
5*4*3 =
60

Answer 2

If the order of the flags doesn't matter, I got 10.

Assume that your five flags are A, B, C, D, and E. These are the possible combinations:
ABC BCD CDE
ABD BCE
ABE BDE
ACD
ACE
ADE

If order matters, however, then think of that as choosing 3 objects from 5 with replacement. The "formula" for that is n^r. n is the number of objects total (5) and r is the number you're choosing (3). So 5^3 = 125.

I just want to add that permutations (as mentioned in some above posts) don't take into account that you're choosing from 5 flags for each combination. In a permutation, once you've chosen something you leave it out of the objects to choose from. In this case, that doesn't work at all since then you'd only be able to make one combination.

Hope that helps!

Answer 3

5•4•3 = 60

Answer 4

Depends. Assume the flags are colored red-white-blue-orange-green. Is red-blue-green the same signal as green-red-blue? If it is, then the answer is a combination... 5!/(3!*2!) = 10, otherwise it is a permutation... 5!/2! = 60

Answer 5

10......this assumes that using 1, 2, 3 is the same as 3, 1, 2 and 2, 1, 3..... so this is just counted once.... I dont see where u have specified.....

Answer 6

5*4*3 assuming that order is important.
If order is not important, then you have to divide by something...but I forgot what. I think you would have to divide by 3.

Answer 7

big difference, i got 9