(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If k people are seated in a random manner in a row containing n seats (n>k), what is the probability that the people will occupy k adjacent seats in the row?

I realize that there are n choose k sets of k seats to be occupied, and that there are n-k+1 sets of k adjacent seats. So the probability that I'm looking for is:

(n-k+1)/(n choose k)

What I don't understand is how the above probability simplifies to:

[(n-k+1)!k!]/n!

Can someone please explain? Thanks.

2. Relevant equations

(^{n}_{k}) = n choose k = n!/[(n-k)!k!]

3. The attempt at a solution

(n-k+1)/(n choose k) = [(n-k+1)(n-k)!k!]/n!

Not sure what to do from here.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Basic combinations problem

**Physics Forums | Science Articles, Homework Help, Discussion**