Combinations and Permutations

rcwitt · 2011-01-20 07:17:04

Me again! I have the following problem and I have arrived at the following answer. I have some doubts about my answer, but I can't seem to put my finger on what is wrong. The answer just seems to be too high. Hopefully, someone here can take a look and see if it is just my self-doubt or if there is an error I can't see.

Problem:
"A computer with an old processor locks up if more than 4 applications are running simultaneously. If the owner has 20 applications stored in his program file, how many different sets of 4 can he run, so that his computer does not lock up?"

Here is what I have so far:

Using the formula for calculating combinations

n = Total number of programs = 20

r = Possible combinations = 4

Does this sound right? I am fairly sure that my math is right. But that seems like an incredible large number of possible combinations of 4 from a set of 20.

Charlie

bobbym · 2011-01-20 07:19:50

Hi Charlie;

You are right about 20 choose 4 but you have made a mistake in calculating it.

rcwitt · 2011-01-20 07:25:08

Bobby,
Can you give me a hint that would lead me to where I made the mistake? I have checked and rechecked with my calculator and can't find it. Maybe I am just blind to it - LOL.

Charlie

bobbym · 2011-01-20 07:27:04

Also you could have saved yourself much hard work.

rcwitt · 2011-01-20 07:28:15

I keep wondering if I should have used the formula for possible permutations:

The answer would be smaller.

Charlie

Bob · 2011-01-20 07:28:31

hi Charlie,

OK up to the final calculation.

When you do 2.43...*10^18/5.02...*10^14 don't forget that your calculator will do * rather than / at the last step.

Re-do as 2.43...*10^18/( 5.02...*10^14) or 2.43...*10^18/5.02.../ 10^14 and it'll come out ok.

To avoid big numbers, I simplified the factorials and got

Then I cancelled the fractions and end up with

Both methods lead to the same result.

edit I see a few posts have got in while I've been typing.

Answer to your question about permutations is no. Your original answer was ok up to the last calc.

Bob

Last edited by Bob (2011-01-20 07:30:01)

bobbym · 2011-01-20 07:28:50

Hi Charlie;

Do it like this from step 1:

I keep wondering if I should have used the formula for possible permutations:

Yes, it would have been smaller than your first answer but it would not be correct. You used the right formula.

Bob · 2011-01-20 07:32:45

hi bobbym,

How are you? I agree with your answer.

Bob

bobbym · 2011-01-20 07:34:25

Hi Bob;

Did not see you. I am fine except I am freezing. How are you?

rcwitt · 2011-01-20 07:34:30

Now I feel like an idiot! I guess I'm trying to make this a lot more complicated than it has to be. Thanks again for your help.

Charlie

bobbym · 2011-01-20 07:35:44

Hi Charlie;

Never feel like an idiot when missing a combinatorics or probability problem. They get everybody!

Hello to Bob, answered your post up above.

Bob · 2011-01-20 07:46:10

hello Charlie and bobbym,

Charlie: Easy mistake to make ... you'd think calculators would be clever enough by now to tell you when you're making this error. Your maths was good; just the sums that went wrong. The important thing is you realised the answer had to be wrong. That's a very useful skill. Better to make it now, and learn from it, than to do it for the first time in an exam.

bobbym: The temperature here in Essex has gone up and we've had loads of rain instead. Had to drive through water up to the sills two days ago; that was scary. Apparently, December was the coldest on record.

Bob

bobbym · 2011-01-20 07:54:25

Glad it eased up. It is warmer here too but still not what I like.

Math Is Fun Forum

#1 2011-01-20 07:17:04

Combinations and Permutations

#2 2011-01-20 07:19:50

Re: Combinations and Permutations

#3 2011-01-20 07:25:08

Re: Combinations and Permutations

#4 2011-01-20 07:27:04

Re: Combinations and Permutations

#5 2011-01-20 07:28:15

Re: Combinations and Permutations

#6 2011-01-20 07:28:31

Re: Combinations and Permutations

#7 2011-01-20 07:28:50

Re: Combinations and Permutations

#8 2011-01-20 07:32:45

Re: Combinations and Permutations

#9 2011-01-20 07:34:25

Re: Combinations and Permutations

#10 2011-01-20 07:34:30

Re: Combinations and Permutations

#11 2011-01-20 07:35:44

Re: Combinations and Permutations

#12 2011-01-20 07:46:10

Re: Combinations and Permutations

#13 2011-01-20 07:54:25

Re: Combinations and Permutations

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