# Combinations! How many.

by Elruso
Tags: combinations
 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.
 Sci Advisor HW Helper Thanks P: 25,228 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?
 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.
PF Gold
P: 1,125
Combinations! How many.

 Quote by 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.
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.
Emeritus
PF Gold
P: 16,091
 Quote by 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.
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,
$$\binom{9}{2 \ 2 \ 2 \ 1 \ 1 \ 1} .$$
HW Helper
Thanks
P: 25,228
 Quote by Hurkyl Did you notice those are the same thing? Incidentally, it seemed most clear to me to write the answer as9! / (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.
 Emeritus Sci Advisor PF Gold P: 16,091 Ah, right. This is what was written:C(9,2)*C(7,2)*C(5,2)*3*2*1and this is what I thought I read:C(9,2)*C(7,2)*C(5,2)*3!*2!*1!

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