Question

How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?

Answer 1

Total number of red flags = 4
Total number of white flags = 2
Total number of green flags = 3
We have to arrange 9 flags, out of which 4 are of red, 2 are white and 3 are green
So, total number of signals = $\frac{9!}{4!2!3!}$
$\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!\times 2\times 3\times 2}$=$9\times 4\times 7\times 5$
= 1260
Hence, total number of signals = 1260.