I how many ways can the letters PARENT be arranged if F and A must be side to side??
I'm assuming you mean "PA" side by side.........
These can occupy any of 5 positions......and for each of these they can be arranged in 2 ways - PA or AP.....
And for all these arangements, the other four letters can be arranged in 4! = 24 ways......so
5 * 2 * 24 =
10 * 24 =
240 different arrangements, if "P" and "A" have to remain together