Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In an experiment E, nine people are asked their birth MONTH, and the nine responses are then written down. All outcomes are equally likely.

Find the probability of the event B = {NO TWO people are born in the same month.}

I know the sample space is 12^9. But i cant figure out how to get the size of B.

I know it is (12)sub9 or 12!/3! because i have the answer key. But I can't figure out why. The answer key doesn't explain. Why is the answer not just 12 choose 9? I feel the answer is 12 choose 9 because you are picking 1 month for each person, without replacement to deal with the restriction, and there are 9 people.

share|improve this question
    
12!/3! is huge. I'm pretty sure that can't be the solution. –  Newb Oct 28 '13 at 5:05
    
That isn't the probability, it's the size of B according to the answer key. –  mashedtatoes Oct 28 '13 at 5:06
    
If the sample space is $12^9$, that means you're treating the nine responses as distinguishable (e.g., maybe everyone writes their name as well). So "January and eight Februaries" is a different outcome than "four Februaries, a January, and four more Februaries". In that case, the number of outcomes where no two people share a month should be ${{12}\choose{9}}$ (choose the months) times $9!$ (choose the order), or $12! / 3!$. –  mjqxxxx Oct 28 '13 at 5:11
    
Now that makes perfect sense! I didn't think about the ordering. Thank you! –  mashedtatoes Oct 28 '13 at 6:12

1 Answer 1

Another way to solve this problem is to think sequentially. What's the probability of having all different birthmonths with just 1 person? 1 (duh). What if we add another person? What's the probability that this new person has a different birthmonth from everybody else? 11/12. If we keep going we see the answer is:

$$ \frac{12}{12} \times\frac{11}{12} \times \ldots \times \frac{4}{12} \approx .015 $$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.