Register to reply

Combinations! How many.

by Elruso
Tags: combinations
Share this thread:
Elruso
#1
Jun2-07, 11:25 AM
P: 5
1. The problem statement, all variables and given/known data
How many letter combinations with 9 letters are you able to make with following letters : M-A-T-E-M-A-T-I-K?


2. Relevant equations
Well its pretty obvious you need to use Combinations.

Please explain how you solve this problem, don't write use combinations .
I need to know how you think and from which angle you "attack" the problem.
Phys.Org News Partner Science news on Phys.org
Security CTO to detail Android Fake ID flaw at Black Hat
Huge waves measured for first time in Arctic Ocean
Mysterious molecules in space
Dick
#2
Jun2-07, 04:31 PM
Sci Advisor
HW Helper
Thanks
P: 25,246
You have 9 letter positions to fill. First lets place the M's. There are two of them, so I have C(9,2) ways. Now lets do the A's. There 2 of them and 7 places left to fill, so I have C(7,2) ways. So far I've got C(9,2)*C(7,2). Can you finish?
Elruso
#3
Jun3-07, 03:34 AM
P: 5
So iit´s C(9,2)*C(7,2)*C(5,2)*3*2*1?

In my math book the answer is C(9,2)*C(7,2)*5!..... which i find a little strange.

danago
#4
Jun3-07, 04:04 AM
PF Gold
P: 1,131
Combinations! How many.

Quote Quote by Elruso View Post
So iitīs C(9,2)*C(7,2)*C(5,2)*3*2*1?

In my math book the answer is C(9,2)*C(7,2)*5!..... which i find a little strange.
When i did it, i got the same answer as you, and then to check, i got mathematica to output every single permutation of those letters into a list. That list contained 45360 elements, so unless ive misunderstood the question, it seems that you may be right.
Hurkyl
#5
Jun3-07, 04:07 AM
Emeritus
Sci Advisor
PF Gold
Hurkyl's Avatar
P: 16,092
Quote Quote by Elruso View Post
So iit´s C(9,2)*C(7,2)*C(5,2)*3*2*1?

In my math book the answer is C(9,2)*C(7,2)*5!..... which i find a little strange.
Did you notice those are the same thing?

Incidentally, it seemed most clear to me to write the answer as
9! / (2! * 2! * 2!),
or, as a multinomial coefficient,
[tex]\binom{9}{2 \ 2 \ 2 \ 1 \ 1 \ 1} .[/tex]
Dick
#6
Jun3-07, 08:47 AM
Sci Advisor
HW Helper
Thanks
P: 25,246
Quote Quote by Hurkyl View Post
Did you notice those are the same thing?

Incidentally, it seemed most clear to me to write the answer as
9! / (2! * 2! * 2!),
or, as a multinomial coefficient,
[tex]\binom{9}{2 \ 2 \ 2 \ 1 \ 1 \ 1} .[/tex]
They aren't the same thing. They differ by a factor of two. Whoever wrote the solution seems to have miscounted the number of doubled letters.
Hurkyl
#7
Jun3-07, 09:32 AM
Emeritus
Sci Advisor
PF Gold
Hurkyl's Avatar
P: 16,092
Ah, right. This is what was written:
C(9,2)*C(7,2)*C(5,2)*3*2*1
and this is what I thought I read:
C(9,2)*C(7,2)*C(5,2)*3!*2!*1!


Register to reply

Related Discussions
Combinations ice cream math Calculus & Beyond Homework 6
How Many Different Combinations? Precalculus Mathematics Homework 11
Sum of Combinations Set Theory, Logic, Probability, Statistics 12
Four tires to mount on a car these can be mounted Set Theory, Logic, Probability, Statistics 3
Combinations and subset help Introductory Physics Homework 4