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
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?
12 Comments • Newest first
[quote=MoldyPeanut]@Itachi9821: Then you should write the instructions too.[/quote]
That's all the question wrote =.= I WROTE EVERYTHING THE QUESTION SPECIFIED
it using those combination thing i learn last semester
more notably it going to use combination permutation i believe not the other one
[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
... The people who thought they were smart with 5!/2! obviously didn't read the question </3
not five letter arrangements of MOLLY, THREE
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
[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!
You would not be able to get 60 because THERE ARE TWO "L"
[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.
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!
what grade are you in o.o
what? how does this make sense?
Google it, I guess.