Question

How many different signals can be made by hoisting two yellow flags, three green flags, and five red flags on a ship's mast at the same time? I tried doing (11 C 2)(11 C 3)(11 C 5) and that doesn't work.

Answer 1

What does a signal mean? Does 2 yellow and 3 red flags mean the same thing regardless of where they are?

Assuming, the only thing that matters is how many flags there are of each colour the answer is 3x4x6=72.

The reasoning goes like this: You can chose the number of yellow flags 3 ways: You can chose either no yellow flags, 1 yellow flag or 2 yellow flags.
You can chose the number of green flags 4 ways (3+1 for no green flags)
You can chose the number of red flags 6 ways.

Answer 2

if they were all different it would be \(10!\) but since you cannot tell for example one red from another it should be
\[\frac{10!}{5!3!2!}\]

Answer 3

That's right. Thanks! :)

Answer 4

btw there are ten flags, not eleven right?

Answer 5

There are ten. I just accidentally typed it in as 11.

Answer 6

k