Question

How many different signals can be made by $5$ flags from $8$ flags of different colours?

• A. $6140$
• B. $6720$
• C. $7340$
• D. $8200$

Answer 1

The correct option is B $6720$

The number of ways of arranging $5$ flags out of $8$ flags of different colours
$={}^8{P}_5=\frac{8!}{(8-5)!}=\frac{8!}{3!}=\frac{\mathrm{8.7.6.5.4.3}!}{3!}=6720.$