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Help with Math Contest Question

How many different three letter arrangements can you make using the letters in the word "MOLLY"?
A. 6
B. 30
C. 33
D. 60
E. 120

The answer is C but why?

March 22, 2012

12 Comments • Newest first

Itachi9821

[quote=MoldyPeanut]@Itachi9821: Then you should write the instructions too.[/quote]

That's all the question wrote =.= I WROTE EVERYTHING THE QUESTION SPECIFIED

Reply March 22, 2012
cyber935

it using those combination thing i learn last semester
more notably it going to use combination permutation i believe not the other one

Reply March 22, 2012
Itachi9821

[quote=MoldyPeanut]There's a difference between combinations and permutations.
You should specify. There's a distinction between the two.

If you wanted a combination of what you could make out of MOLLY
you'd have 5 C 2 which is equivalent to (5!)/(3!)(2!)
Combination wise, it's 30.
Using permutations, you get 60.

Specify what you need.[/quote]

I specified what was written inside the book

Reply March 22, 2012
evelynmak

... The people who thought they were smart with 5!/2! obviously didn't read the question </3
not five letter arrangements of MOLLY, THREE

Reply March 22, 2012
MtsGraduate

MOLLY = 12334
12334

Prefix Ending
12 3 4
13 2 3 4
14 2 3
21 3 4
23 1 3 4
24 1 3
31 2 3 4
32 1 3 4
33 1 2 4
34 1 2 3
41 2 3
42 1 3
43 1 2 3

Prefix with no 3 has 2 endings
Prefix with 3 has 3 endings

6*2 = 12
7*3 = 21
12+21 = 33

Reply March 22, 2012
Itachi9821

[quote=TheTuvvo]Number of combinations using L only once (M O L Y ): 4*3*2 = 24

Number of combinations using one letter from (M O Y) and both LL: 3 (eg. MLL LML LLM) = Now do that for the other 2 letters as well: (OLL LOL LLO) and (YLL LYL LLY) = total of 9 combinations.

24 + 9 = 33.[/quote]

Wow that makes sense! THANKS!

Reply March 22, 2012
Itachi9821

You would not be able to get 60 because THERE ARE TWO "L"

Reply March 22, 2012
radkai

[quote=Keey]oh, this is easy,

it is 5!/2!

which is 120/2, which is 60. D.

the way you get this is by permutations, see there are 5 ways you can arrange the letters MOLLY in any order, but since there are two of the same letter, you must divide by how many repeating letters there.

for instance, MISSISSIPPI

how many different ways can i arrange this?

well since there are 11 letters, it would be 11!

but the letter 's' repeats four times, the letter 'i' repeats four times, and the letter 'p' repeats two times

so it would be 11! / 4!4!2![/quote]

You read problem wrong. It wants 3-letter combination, not the original length.

Reply March 22, 2012
Keey

oh, this is easy,

it is 5!/2!

which is 120/2, which is 60. D.

the way you get this is by permutations, see there are 5 ways you can arrange the letters MOLLY in any order, but since there are two of the same letter, you must divide by how many repeating letters there.

for instance, MISSISSIPPI

how many different ways can i arrange this?

well since there are 11 letters, it would be 11!

but the letter 's' repeats four times, the letter 'i' repeats four times, and the letter 'p' repeats two times

so it would be 11! / 4!4!2!

Reply March 22, 2012
J9ssica

what grade are you in o.o

Reply March 22, 2012
lipperman123

what? how does this make sense?

Reply March 22, 2012
Dhaos

Google it, I guess.

Reply March 22, 2012