# Probability of picking rooms

Suppose there are 15 rooms among which a person in present in one room. If i pick 5 rooms out of them, what is the probability that the person is present in one of the 5 rooms selected?

No of ways we can pick 5 rooms: 15C5, So answer could be x/15C5

Where am i stuck is how to figure out x? Among 15C5 selections, which of them will contain that specific room in which the person is there?

• Please show what you have tried and where you are stuck. – Gummy bears Sep 23 '15 at 4:48
• Wouldn't this just be $\frac{1}{3}$, since we are splitting up the 15 total rooms into three sets of 5 rooms, and then seeing if the person is in one of the three sets? I feel like I'm missing something though... – Brevan Ellefsen Sep 23 '15 at 4:51
• @BrevanEllefsen Nope. The five rooms aren't fixed. It's not like there are three groups of five to chose from. We have tho chose all the five members of the group. – Gummy bears Sep 23 '15 at 5:13
• @Gummybears oh ya, combinations... duh. I really dropped the ball on that one. Time to take another probability course... been way too focused on real analysis.... – Brevan Ellefsen Sep 23 '15 at 5:19

Hint

There is only one way to choose the occupied room, what about the rest ?

Why confused ? $Pr = {1\choose 1}{14\choose4} / {15\choose 5}$
Of course, you can leave out the ${1\choose 1}$ , but it shows exactly what you did .