Circular permutation and Permutation of N dissimilar items

[jp.jprasanna]

hi - Can some one help me understand the below formulas pls with an example or 2!

The total number of permutations of n dissimilar things taken r at a time with repetitions = n^r

- How can we post 3 dissimilar letter in 4 different box!?

1 letter has 4 positions so has the 2nd and 3rd letter?

so 4 * 4 * 4 that is essentially 4^3

In case we have 3 similar letters in 4 different box? Is the below equation correct

4! / 3! * 1!

Do you have any GMAT like problems / GMAT problems I can use to see how it works?

No. of circular permutations of n things taken all at a time = (n - 1)!

4 people can be arranged in a round chair !

(4-1)! = 3!

But Do you have any GMAT like problems / GMAT problems I can use to see how it works?


No. of circular permutations of n different things taken r at a time = nPr/r

I have no idea why we divide here by r?

Cheers

[tim]

"The total number of permutations of n dissimilar things taken r at a time with repetitions = n^r
- How can we post 3 dissimilar letter in 4 different box!?
1 letter has 4 positions so has the 2nd and 3rd letter?
so 4 * 4 * 4 that is essentially 4^3"

This approach is correct, but the scenario you describe is not consistent with the description you gave - with repetition, this example would essentially allow letter 1 to go in three different boxes if it were chosen three times in a row. Perhaps a better example would be to ask how many sequences of three rolls you could get from a 4-sided die.

"In case we have 3 similar letters in 4 different box? Is the below equation correct
4! / 3! * 1! "

This works as long as no box can contain more than one letter.

"Do you have any GMAT like problems / GMAT problems I can use to see how it works?"

There are quite a few of these problems in our Word Translations strategy guide (4th edition) or Number Properties (5th edition).

"No. of circular permutations of n things taken all at a time = (n - 1)!
4 people can be arranged in a round chair !
(4-1)! = 3! "

Correct, but I've never seen any GMAT problems that utilize this concept.

"No. of circular permutations of n different things taken r at a time = nPr/r
I have no idea why we divide here by r?"

I'm not sure what you mean by circular permutations, but this formula doesn't apply to any scenario I'm aware of.