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# How many words of 2 distinct vowels and 3 distinct consonant

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How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

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02 Sep 2005, 17:24
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How many words of 2 distinct vowels and 3 distinct consonants can be made using the English Alphabet?

[Reveal] Spoiler:
my approach was

C 5 2 * C 21 3 / C 26 5

PLz correct me I am wrong

Last edited by Bunuel on 20 Oct 2013, 22:57, edited 1 time in total.
Renamed the topic and edited the question.
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Re: ps TRICKY Combination PROBLEMS [#permalink]

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02 Sep 2005, 17:46
I am not sure why you are dividing with 26C5, there is no probability involved

IMO the best way is (21C3*5C2)*5!

because if we rearrange each 5 letter words we get 5! different words...
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Re: ps TRICKY Combination PROBLEMS [#permalink]

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20 Oct 2013, 22:35
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If you still need further clarification, it goes like this...

from 5 vowels you need to pick 2 and 21 consonants you need to pick 3

5C2* 21C3 . These 5 letters can be arranged in 5! as they are all distinct , ergo 5C2*21C3*5!
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Re: ps TRICKY Combination PROBLEMS [#permalink]

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20 Oct 2013, 22:36
If you still need further clarification, it goes like this...

from 5 vowels you need to pick 2 and 21 consonants you need to pick 3

5C2* 21C3 . These 5 letters can be arranged in 5! as they are all distinct , ergo 5C2*21C3*5!
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Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

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30 Dec 2013, 05:41
mandy wrote:
How many words of 2 distinct vowels and 3 distinct consonants can be made using the English Alphabet?

[Reveal] Spoiler:
my approach was

C 5 2 * C 21 3 / C 26 5

PLz correct me I am wrong

I got the following

We have a 5 letter word

We need to pick 3 out of 21 consonants and 2 out of 5 vowels

So we have slot method _ _ _ _ _

So it boils down to 5C3 (21*20*19) (5*4*3)

5 ways of arranging the 3 consonants and two vowels * We have 21 options for the first consonant, 20 for the second, 19 for the third since they have to be different and same for vowels

Is this approach correct?

Let me know will you?

Thanks

Cheers!
J
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Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

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02 Jul 2016, 10:33
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Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

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27 Jul 2016, 23:55
please let me know if my approach is wrong
I have solved the question by Fundamental Principle of Counting
vowels{a,e,i,o,u}=5
consonants 26-5=21
In the 5 letter word
2 vowels need to be there along with 3 consonants
for filling vowels
5x4=20 ways/words
for filiing consonants
21x20x19 ways/words
hence the number of ways/words for forming a 5 letter word according to the given conditions will be
20X21X20X19 ways/words
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Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

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24 Aug 2016, 11:25
suramya26 wrote:
please let me know if my approach is wrong
I have solved the question by Fundamental Principle of Counting
vowels{a,e,i,o,u}=5
consonants 26-5=21
In the 5 letter word
2 vowels need to be there along with 3 consonants
for filling vowels
5x4=20 ways/words
for filiing consonants
21x20x19 ways/words
hence the number of ways/words for forming a 5 letter word according to the given conditions will be
20X21X20X19 ways/words

Hi Suramya26,

There are 2 sets here one with 5 vowels {a,e,i,o,u} and other with 21 consonants.
The word formed should have 5 letters in which 2 are vowels and 3 are consonants.

from {a,e,i,o,u} to pick only 2 , there are $$5C2$$ ways.
from 21 consonants to pick 3, there are $$21C3$$ ways.
But the 5 letter word can rearranged in to $$5!$$ ways, (AEBCD is different from ABCDE)

so answer is $$5C2 * 21C3 * 5!$$.
Re: How many words of 2 distinct vowels and 3 distinct consonant   [#permalink] 24 Aug 2016, 11:25
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