Question

from 3 red 2 yellow and 2 green signal flags, how many different signals are possible if we want to make signals by arranging all of them vertically on a flag staff?

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{flags}=7 \\ \mathrm{Number}\mathrm{of}\mathrm{signals}\mathrm{can}\mathrm{be}\mathrm{formed}=\frac{7!}{3!2!2!} \\ =\frac{7\times 6\times 5\times 4\times 3!}{3!\times 2\times 2}=7\times 6\times 5=210\mathrm{ANS}... \end{gathered}$$