Dalia S.

asked • 04/03/14

Solve the following permutation question

How many ways are there to select 11 countries in the United Nations to serve on a council if 1 is selected from a block of 51, 1 are selected from a block of 68 and 9 are selected from the remaining 70 countries?

3 Answers By Expert Tutors


Dalia S.

i keep getting error on my calculator for the other two, possible because the answer is too large... any idea to what they might be?


Kay G.

When I do the first calculation, I get an answer like 51.00000000003 or some weird thing.  But it sounds like you're referring to the factorials that can end up very, very large.  Like 51! is 1.55111875x1066.  (I once wrote out 69 decimal places on a piece of paper just to see how very large these numbers are. :-) )
For the 1st two you don't need to worry about it, since when you pick only 1 item, there's n ways to do that, n being the total picked from.  So that's just 51 and 68, without doing any math. 
Perhaps your calculator just can't handle numbers that large?  Mine does them in scientific notation.  If there's a problem with the calculator doing these, you need to find that out and perhaps get a different calculator, so let's go through how you want to solve that.
All calculators are different so I can't give you an exact method.  First see if you have to enter the number or the ! first.  Try 5! - first try entering 5 and then the !, and make sure that works and you don't get a syntax error.  The answer is 120.  Otherwise try ! first and then the 5 but normally it's the the first way.
Then try 70! by itself before trying the whole equation, just to make sure you can get the right answer, which is 1.1978572x10100.  The exponent could easily be different depending on how many decimal places it can hold, so just make sure the initial digits are the same.  If you can't get that on your calculator, then you need to get one that can handle it.  (You should talk to someone at your school about that, in case they have an "approved" list or one you'll need for a future class, etc.  I believe graphing calculators have a way to do these automatically?  But I don't use one.)
If that works, let's make sure you're doing everything within the equation correctly.  That denominator will actually be (9!)(61!).  If you solve that (70-9) first, it'll make running the equation easier.  You can either do it in order, using parenthesis, or the denominator first and put it in memory. 
In other words, if you start with 70!, then divide, make sure you're putting opening and closing parenthesis around the (9!61!).  You probably then still need to hit = or Enter.  You can also do 9!61! first - again, you probably need to hit = or Enter at the end.   Put it in memory, then go back and do 70!, divide, then pull that up from memory.  If you have an ANS key, you can do the denominator, and then immediately do 70! divide by ANS.
(Sometimes it's a good idea to do it more than one way, to make sure you're still getting the same answer.  These are easy to screw up.)
I already wrote the answer to numerator.  Answer to denominator is 1.84190708x1089.  You may have to play around until you get that, so you know how to do it.
Then the 70! / (9!61!) = 60,033,528,560.  If your calculator can't hold that many digits, that right there might be your problem.  And you still have to multiply that by 51 and 68, making it even larger, and that would go into scientific notation.  (You need a calc that can do scientific notation and you need to make sure you know how to read it.)
You may need to sit down with someone in person and work through this.  But there's all the answers so you can at least experiment.


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