Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

P(they all were born in the same month ) = 1 / 12^12 = ???
P(they all were born in different months ) = 12! / 12^12 = ???
P(exactly six of them were born in the same month) =
= 11 * 10 * 9 * 8 * 7 * 6 / 12^12

The probability that each prisoner was born in January, for example
1/12*1/12*1/12....=1/12^12
If we take all months 12*1/12^12
The probability that all were born in different months
12!/12^12
The probability that exactly six of them were born in the same month
12C6/12^12

The probability that each prisoner was born in January, for example 1/12*1/12*1/12....=1/12^12 If we take all months 12*1/12^12 The probability that all were born in different months 12!/12^12 The probability that exactly six of them were born in the same month 12C6/12^12

(1) correct
(2) correct
(3) doubt

any 6 are taken (12C6). they were born in the same month (12). other six people have 11*10*9*8*7*6 chances to be born in different months.

I got the first 2 right but I think that the 3rd question should be worded as: The probability that exactly six of them were born in the same month
and that the 5 others are all born in different months.
Only then will Stoylar's answer's 12C6*12*11*10*9*8*7*6/12^12 will be good. Because, what if 6 have the same birth months but 2, 3 , 4 or 5 others also have another same birth month? I think worded as I said it, then Stoylar's answer would be right. Any thoughts? _________________

I think the 1st one should be 12/(12^12) because there are 12 possible months for everyone to be born on the same month. 1/(12^12) implies that there is only one possible way, but everyone can be born in Jan, Feb, Mar...etc all the way to Dec.

For example, if there are only 3 months in a year (Jan , Feb, Mar) and three people, then the total possible combinations are 3/(3^3).

P1 P2 P3
Jan Jan Jan
Feb Feb Feb
Mar Mar Mar
-----------------
Jan Feb Mar
Jan Mar Feb
Feb Jan Mar
Feb Mar Jan
Mar Jan Feb
Mar Feb Jan
21 more ....

I think the last one should be 12C6*12*11*11*11*11*11*11/12^12. Six can be born in the same month and the other six can be born in the same months too...just not the same month as the first six.

Calnhob, I think your answer should be good. 12C6*12 for 6 having the same birth months, then 11^6 for the other 6 having diff. or same birth months all being accounted for in 11^6. Thus, the final answer, as you said should really be (12C6*11^6) / 12^12. Do you agree that Stoylar's answer represents The probability that exactly six of them were born in the same month and that the 5 others are all born in different months.? _________________