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

Step 1: Write the given values

Given,

Number of red flags $p=4$

Number of white flags $q=2$

Number of green flags $r=3$

$\therefore$Total number of flags $n=4+2+3$

$=9$

Step 2: Estimate the number of signals

The different number of signals that can be made by the given number of flags,

$\frac{n!}{p!\times q!\times r!}=\frac{9!}{4!\times 2!\times 3!}$

$=\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!\times 2\times 3\times 2}$

$=9\times 4\times 7\times 5$

$=1260$

Hence, $1260$ different signals can be made from the given flags.