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I was solving a problem in probability (basic level). The problem is from a text book (Morris H.DeGroot). The problem is as,

if $k$ people are seated random in a row containing $n$ seats ( $n > k$ ). What is the probability that people will occupy $k$ adjacent seats in the row.

My approach of the solution is: Sample space is clearly ${n \choose k}$. Now to get the event's possible outcomes I assume that 'k' adjacent seats are as 1 unit (as all the 'k' should be adjacent) then subtracting 'k' from 'n' and adding 1 unit to 'n' gives $(n-k)+1$. Now from this we just choose '1'. so it will be ${n-k+1 \choose 1}$ .

So the answer is $(n-k+1) \times \frac{1}{{n \choose k}}$. I see that the answer is correct from the text book answers. Is my approach correct? If not please let me know what should be the approach to solve this problem.


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Looks good to me. – Gerry Myerson May 17 '11 at 6:35
Thanks Gerry Myerson – poddroid May 17 '11 at 9:58
up vote 2 down vote accepted

Your answer is correct, and with a very high probability this is the most simple approach you could find :)

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