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sk

Member

Registered: 2006-08-04

Posts: 19

Help me with this problem

How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Help me with this problem

hmmm,  its more complicated than i first though, its not a case of adding permutations, since you can have them in different orders.

: How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are differe

from 12 consonants, the possible list of consonants you can have is

from 4 vowels, the possible list of vowels you can have is

for each list of consonants, it can be combined with each list of vowels in (4+3)! = 5040 ways

that comes to:

11880*24*5040 = 13437004800

my my thats alot of words, ofcourse, few of them would actually be sensical

Last edited by luca-deltodesco (2007-07-09 21:46:06)

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Help me with this problem

for each list of consonants, it can be combined with each list of vowels in (4+3)! = 5040 ways

Nope. It’s only [sup]7[/sup]C[sub]4[/sub] (or [sup]7[/sup]C[sub]3[/sub]) = 35 ways.

So the total number of words is 11880 × 24 × 35 = 9979200. (Still a lot of words though.)

Last edited by JaneFairfax (2007-07-09 23:19:56)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Help me with this problem

Not quite. You're counting things twice there.

You're making order important by using permutations in the lists, but then you're making order important again by saying the number of ways to list C_1, C_2, C_3, C_4, V_1, V_2 and V_3, when you should be saying the number of ways to list C, C, C, C, V, V, V, which is 35.

Alternatively, you could just switch to C's instead of P's in the first steps. Either way, the answer should be 9,997,200.
Also, that first 3 in your final answer looks like a typo.

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Help me with this problem

ah yes, i see where i made my mistake, thanks

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