Take the 2-minute tour ×  I have no idea how to begin the
following problem  Nautical flags are specially designed flags
made up of several colors which can be used to signal from ship
to ship, or ship to shore. Suppose there are 4 red, 5 blue and 8
yellow flags. How many different arrangements can be made if all
the flags must be used on a vertical flag pole?  share|improve
this question It's a trick question -- there is no solid blue
maritime signaling flag. –  Henning Makholm Nov 12 '12 at 0:33
3 Answers 3  up vote 0 down vote accepted  There are a total of
seventeen slots on the flagpole. The red flags can be placed in
$\binom{17}{4}$ ways (we use combinations since the red flags
are indistinguishable from each other). Next, we can place the
five blue flags in $\binom{13}{5}$ ways (since there are only
thirteen remaining spots). Finally, place the eight yellow flags
in $\binom{8}{8}$ ways (which is just one - our only option is
to fill the remaining eights spots with the eight yellow flags.
Thus, there a