Question

Given 7 flags of different colours, how many different signals can be
generated if a signal requires the use of two flags, one below the
other?

Answer 1

No. Of signals generated using two flags one below the other In first there will be 7 flags and in below there will be 6flags,so 7*6=42 ways

Answer 2

Use of permutation so according to problem how to arrange 7 objects taken 2 at a time 
so as there are only two flags be arranged with 7 different colors so the first flag can be arranged in any 7 ways and as for the second flag we have only 6 flag left(as 1 flag is already used) so it can be arranged in 6 ways

 so 7 × 6 = 42 ways it can be arranged