Hi,
I a currently looking at the explanation for the Combinatorics with repetition anagram grids. I am having a hard time understanding when one has to divide the total number of factorials by the one that is no longer need. I cannot tell the difference between doing this to when one must multiply two different kinds of factorials and then divide this from the total number of factorials.
On the problem set for the end of the chapter, I do not understand why question number 3 is solved by multiplying the factorial 2 times factorial 3 and then dividing it by Factorial 5.
The question for your reference is
A men's basketball league assigns every player a two digit number for the back of his jersey. If the league uses only the digits 1-5, what is the maximum number of players that can join the league such that no player has a number with a repeated digit and no two players have the same number?
Thanks,
Dannialles
GRE Forum Archive
4 postsPage 1 of 1
- dddannie6
- Course Students
- Posts: 20
- Joined: Mon May 07, 2012 12:36 pm
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Word Problems - Combinatorics
Hey DDDanie,
I don't actually approve of the anagram grid method, so I'm going to teach you another method. However, it also sounds like you are confused about the difference between order mattering and order not mattering. I'll try to explain that, too. Let's start with the slots method for doing combinatorics.
The Slots Method
1. Find the # of slots.
-- A slot is any point at which you get to make a decision.
2. Fill in each slot with the # of choices at that decision point.
-- If you have to walk through a door, and there are three
doors, that's one slot with a 3 in it.
3. Figure out if Order Matters, Order Doesn't Matter, or a combination of the two (more common on harder questions).
-- If chocolate-vanilla is not the same as vanilla-chocolate,
order matters.
4. If Order Matters, simply multiply all slots together.
5. If Order Doesn't Matter, multiply all slots together, then divide by the # of slots factorial wherever order doesn't matter.
Keep in mind, this is a different method. Do not attempt to mix it with the anagram grid method, because that will confuse everything.
Let's use the new method on your question:
1. There are two slots (We have two choices to make--the two digits on the jersey). We would write this down like so:
_ _
2. We have 5 choices for the first slot, but only 4 choices for the second slot (no repeated digits allowed). We would write this down like so:
5 4
3. Does order matter or not? It matters here, because 54 is not the same as 45. Those are the same two numbers (a 4 and a 5), but the number changes if the order is different.
4. So all we have to do is multiply the slots together:
5 * 4 = 20
Let me know if that helps!
-t
I don't actually approve of the anagram grid method, so I'm going to teach you another method. However, it also sounds like you are confused about the difference between order mattering and order not mattering. I'll try to explain that, too. Let's start with the slots method for doing combinatorics.
The Slots Method
1. Find the # of slots.
-- A slot is any point at which you get to make a decision.
2. Fill in each slot with the # of choices at that decision point.
-- If you have to walk through a door, and there are three
doors, that's one slot with a 3 in it.
3. Figure out if Order Matters, Order Doesn't Matter, or a combination of the two (more common on harder questions).
-- If chocolate-vanilla is not the same as vanilla-chocolate,
order matters.
4. If Order Matters, simply multiply all slots together.
5. If Order Doesn't Matter, multiply all slots together, then divide by the # of slots factorial wherever order doesn't matter.
Keep in mind, this is a different method. Do not attempt to mix it with the anagram grid method, because that will confuse everything.
Let's use the new method on your question:
A men's basketball league assigns every player a two digit number for the back of his jersey. If the league uses only the digits 1-5, what is the maximum number of players that can join the league such that no player has a number with a repeated digit and no two players have the same number?
1. There are two slots (We have two choices to make--the two digits on the jersey). We would write this down like so:
_ _
2. We have 5 choices for the first slot, but only 4 choices for the second slot (no repeated digits allowed). We would write this down like so:
5 4
3. Does order matter or not? It matters here, because 54 is not the same as 45. Those are the same two numbers (a 4 and a 5), but the number changes if the order is different.
4. So all we have to do is multiply the slots together:
5 * 4 = 20
Let me know if that helps!
-t
- nazmul.2000
- Students
- Posts: 2
- Joined: Mon Sep 16, 2013 7:55 pm
Re: Word Problems - Combinatorics
Tommy,
Your slot method is so much helpful. Thanks a lot.
Your slot method is so much helpful. Thanks a lot.
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Word Problems - Combinatorics
Glad to help!
-t
-t
4 posts Page 1 of 1