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?
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There is only one way to choose the occupied room, what about the rest ?
Answer:
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 .
$\endgroup$ 1 $\begingroup$First, chose the single door that has the person behind it. Then, the four remaining doors can be chosen in any fashion.
Basically, how will you chose 4 doors from a total of 14 doors (as we have already chosen the one with the person behind it)?
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