# Permutations and Combinations

• May 10th 2012, 02:20 PM
uperkurk
Permutations and Combinations
So I havea really bad worded question in my opinion... It reads

1a) Given the word leak, calculate the number of permutations:

I wrote 24 because 4! = 24

1b) Calculate the number of 2-letter unordered combinations:

I wrote 6 because 24 / 2 = 12 then half 12 because it's asking for unordered combinations.

2c) By writing out all the permutations and all the 2-letter unordered
combinations, show that the two methods described above give the same result,
and that the number of results are consistent with the numbers you calculated
above:

But they don't give the same result.... one gives 24 and the other 6.... what is it asking for exactly?
• May 10th 2012, 02:36 PM
Plato
Re: Permutations and Combinations
Quote:

Originally Posted by uperkurk
So I havea really bad worded question in my opinion... It reads
1a) Given the word leak, calculate the number of permutations:
I wrote 24 because 4! = 24 CORRECT

1b) Calculate the number of 2-letter unordered combinations:
I wrote 6 because 24 / 2 = 12 then half 12 because it's asking for unordered combinations.

2c) By writing out all the permutations and all the 2-letter unordered
combinations, show that the two methods described above give the same result,
and that the number of results are consistent with the numbers you calculated
above: But they don't give the same result.... one gives 24 and the other 6.... what is it asking for exactly?

I agree this a poorly put question.

But unordered combination are $\displaystyle \binom{4}{2}=\frac{4!}{2!\cdot 2!}=6$.

I do not understand what 2c) says.
There 24 permutations and 6 combinations.