1. ## arrangement probability

hello, this was a multiple choice question.

The letters P, Q ,R,S,T and U are arranged randomly in a line. what is the probability that P and Q are next to each other.

A) $\frac{2X5!}{6!}$

B) $\frac{2X6!}{5!}$

C) $\frac{5X2!}{6!}$

D) $\frac{5X6!}{2!}$

i think i can eliminate B and D because i would not get a decimal for my answer but am not too sure anyway.
can someone please show me how this question is solved..

2. There are 6! permutations of the 6 letters so you know that has to be your denominator.

If you join the two letters they can be in seats 1&2, 2&3, 3&4, 4&5, or 5&6.

So there are 5 seat combinations that they can occupy and they can go QP or PQ so I believe the answer is 5!*2! / 6!.