Question

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

• A. 210
• B. 215
• C. 220
• D. 225

Answer 1

The correct option is A 210

Here $n=3+2+2=7$
$p_1=3,p_2=2$ and $p_3=2$
$\therefore$ Required number of different signals
$=\frac{n!}{p_1!p_1!p_1!}=\frac{7!}{3!2!1!}\frac{\mathrm{7.6.5.4}}{2.2}$
$=\mathrm{7.6.5}=210$