Combinations! How many letter combinations can you make with 9 letters?

[Elruso]

Combinations! How many...

Homework Statement

How many letter combinations with 9 letters are you able to make with following letters : M-A-T-E-M-A-T-I-K?

Homework 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.

 

[Dick]

You have 9 letter positions to fill. First let's place the M's. There are two of them, so I have C(9,2) ways. Now let's 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]

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]

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.

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 I've misunderstood the question, it seems that you may be right.

 

[Hurkyl]

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,

$$\binom{9}{2 \ 2 \ 2 \ 1 \ 1 \ 1} .$$​

 

[Dick]

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,

$$\binom{9}{2 \ 2 \ 2 \ 1 \ 1 \ 1} .$$​

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]

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!​