# Math Help - Permutations with Repetition help (2 Questions)

1. ## Permutations with Repetition help (2 Questions)

Here are 2 problems I am currently stuck on.

A) In the card game for bridge, 2 cards are dealt to 4 people who are called North, South, East and West. A 52 letter "word" consisting of 13 N's, 13 S's, 13 E's and 12 W's will tell you who has what card. For example, if a word begins with NEEWS...., the North has the ace of spades, East has the 2 and 3 of spades, West has the 4 of spades, South has the 5 of spades and so on. How many such arrangements are there?

B) A group of 12 friends goes to a cinema complex that is showing 6 different movies. If the group splits into subgroups, how many subgroup combinations are possible. FOR THIS PROBLEM A HINT WAS GIVEN: You can form words that use 12 x's to tally the groups and lines to separate the x's into the 12 movies. I AM NOT ALLOWED TO USE THE FORMULA (n+r -1)C(n).

Thank You.

2. ## Re: Permutations with Repetition help (2 Questions)

Originally Posted by jamman751
A) In the card game for bridge, 2 cards are dealt to 4 people who are called North, South, East and West. A 52 letter "word" consisting of 13 N's, 13 S's, 13 E's and 12 W's will tell you who has what card. For example, if a word begins with NEEWS...., the North has the ace of spades, East has the 2 and 3 of spades, West has the 4 of spades, South has the 5 of spades and so on. How many such arrangements are there?

B) A group of 12 friends goes to a cinema complex that is showing 6 different movies. If the group splits into subgroups, how many subgroup combinations are possible. FOR THIS PROBLEM A HINT WAS
You have a real problem with language here. I have no idea what part A) means. Can you restate it in simple terms without gobligook?

For part B), it seems that as stated the answer is $6^{12}$. That is the number of functions from a set of twelve to a set of six.

But I do not think that is what you are asking
If that is correct, then what you are asking?

3. ## Re: Permutations with Repetition help (2 Questions)

That has caused me a great deal of confusion as well. I copied part A word for word and I can't figure out what its asking for.

Also, the answer to B is 6188.

4. ## Re: Permutations with Repetition help (2 Questions)

Originally Posted by jamman751
That has caused me a great deal of confusion as well. I copied part A word for word and I can't figure out what its asking for. Also, the answer to B is 6188.
Well I feel for you! In my opinion, whoever set these questions is incompetent.
That may not be true if you are translating this into English from some other language.
But if not, you need to report this competency to your educational authority.

5. ## Re: Permutations with Repetition help (2 Questions)

Originally Posted by jamman751
Here are 2 problems I am currently stuck on.

A) In the card game for bridge, 52 cards are dealt to 4 people who are called North, South, East and West. A 52 letter "word" consisting of 13 N's, 13 S's, 13 E's and 13 W's will tell you who has what card. For example, if a word begins with NEEWS...., the North has the ace of spades, East has the 2 and 3 of spades, West has the 4 of spades, South has the 5 of spades and so on. How many such arrangements are there?

Thank You.
I made a couple of small changes above. The question seems to be asking for the number of possible bridge deals which whether you think about those 'words' or not is $\frac{52!}{(13!)^4}$.