Question

How many different signals can be transmitted by arranging $2$ red, $3$ yellow and $2$ green flags on a pole? (Assume that all the $7$ flags are used to transmit a signal).

Answer 1

There are $3$ red, $2$ yellow $2$ green flags

Total number of way to arrange if all are different $=7!$

But $3$ reds are same and $2$ yellow $2$ green are also same so

the number of ways $=\frac{7!}{3!2!2!}=210$