# combs maths help (1 Viewer)

#### B1andB2

##### oui oui baguette
Hey!
For the question 'How many ways can u choose 5 letters from MAMMOTH, i tried doing cases- case 1: all Ms, case 2: 2 Ms and Case 3: 1 M but im not getting the answer. Are my cases incorrect?

#### TheShy

##### Active Member
So out of 5 letters to choose out of 7 total letters : _ _ _ _ _. Number of ways to do that is 7P5, which should = to 2520. However hte word MAMMOTH has the letter M repeating 3 times, so you would divide by 3!. Thus the answer should be (I think) 2520/3!. Check with the answers cos im not 100% sure

#### B1andB2

##### oui oui baguette
So out of 5 letters to choose out of 7 total letters : _ _ _ _ _. Number of ways to do that is 7P5, which should = to 2520. However hte word MAMMOTH has the letter M repeating 3 times, so you would divide by 3!. Thus the answer should be (I think) 2520/3!. Check with the answers cos im not 100% sure

#### idkkdi

##### Well-Known Member
Hey!
For the question 'How many ways can u choose 5 letters from MAMMOTH, i tried doing cases- case 1: all Ms, case 2: 2 Ms and Case 3: 1 M but im not getting the answer. Are my cases incorrect?
MAMMOTH

Choose 5 letters, means leaving 2 out. Alternatively just choose the two left out. M-M,A,O,T,H. A-O,T,H. O-T,H. T-H.

#### TheShy

##### Active Member
Case 1: One M's - choose the other 4 letters from AOTH: 4C4 = 1
Case 2: Two M's - choose the other 3 letters from AOTH: 4C3 = 4
Case 3: Three M's - choose the other 2 letters from AOTH: 4C2 = 6

Total = 4+6+1 = 11

#### TheShy

##### Active Member
How does this 4C stuff work? Haven't done combinatorics properly yet, I just intuition them out.
Combinations is similar to permutations, just that the order matters. Permuation is when the order doesnt matter, and combination is when the order does matter. Combinations are in the form nCr, which is $\bg_white \frac{n!}{r!(n-r)!}$. The 4C4 means that from 4 choose 4, and 4C3 means from 4 choose 3 and so on. They might also write in another way, that is fraction without the horizontal bar : $\bg_white \binom{n}{r}$

#### idkkdi

##### Well-Known Member
Combinations is similar to permutations, just that the order matters. Permuation is when the order doesnt matter, and combination is when the order does matter. Combinations are in the form nCr, which is $\bg_white \frac{n!}{r!(n-r)!}$. The 4C4 means that from 4 choose 4, and 4C3 means from 4 choose 3 and so on. They might also write in another way, that is fraction without the horizontal bar : $\bg_white \binom{n}{r}$
I meant the proof for that. Dw, just remembered I wrote up one last yr for content.

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#### B1andB2

##### oui oui baguette
Case 1: One M's - choose the other 4 letters from AOTH: 4C4 = 1
Case 2: Two M's - choose the other 3 letters from AOTH: 4C3 = 4
Case 3: Three M's - choose the other 2 letters from AOTH: 4C2 = 6

Total = 4+6+1 = 11
when you choose the Ms, how come you don't include choosing the M out of the 3 so like 3C1 ?

#### TheShy

##### Active Member
when you choose the Ms, how come you don't include choosing the M out of the 3 so like 3C1
Cause they are repeating. If you had MMM theres only one way since they are considered the same. If that makes sense

#### idkkdi

##### Well-Known Member
when you choose the Ms, how come you don't include choosing the M out of the 3 so like 3C1 ?
Because it's the same letters. M1, M2, M3 sure. But in this case, there is no point of difference.

#### idkkdi

##### Well-Known Member
Cause they are repeating. If you had MMM theres only one way since they are considered the same. If that makes sense
You beat me by less than a second.

#### B1andB2

##### oui oui baguette
Cause they are repeating. If you had MMM theres only one way since they are considered the same. If that makes sense
Because it's the same letters. M1, M2, M3 sure. But in this case, there is no point of difference.
so does this also apply to the cases where there are two Ms and one M?

#### Drdusk

##### Moderator
Moderator
when you choose the Ms, how come you don't include choosing the M out of the 3 so like 3C1 ?
This is because your kind of keeping the M’s ‘constant’ and choosing everything around it.

Suppose you do something like 3C1. That means out of the 3 M’s your choosing one of them. All the M’s are the exact same thing though so it does not matter which one you choose because the combination of letters will still be the same. So like if you choose M1, A,O,T, H, then M1 can be replaced by M2 or M3 but that does not change the combination because all the M’s are the same!

So yes it obviously applies to cases of 2 M’s and 1 M

#### B1andB2

##### oui oui baguette
This is because your kind of keeping the M’s ‘constant’ and choosing everything around it.

Suppose you do something like 3C1. That means out of the 3 M’s your choosing one of them. All the M’s are the exact same thing though so it does not matter which one you choose because the combination of letters will still be the same. So like if you choose M1, A,O,T, H, then M1 can be replaced by M2 or M3 but that does not change the combination because all the M’s are the same!

So yes it obviously applies to cases of 2 M’s and 1 M
Thank you for the clarification. That was very helpful. So would i do something like 3C1 for the arranging questions?

#### B1andB2

##### oui oui baguette
Thanks everyone for the help!

nah brah its 480
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