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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] New post 02 Sep 2005, 16:24
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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, 21:57, edited 1 time in total.
Renamed the topic and edited the question.
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Re: ps TRICKY Combination PROBLEMS [#permalink] New post 02 Sep 2005, 16:46
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] New post 20 Oct 2013, 21:35
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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] New post 20 Oct 2013, 21:36
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] New post 30 Dec 2013, 04:41
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 :)
Re: How many words of 2 distinct vowels and 3 distinct consonant   [#permalink] 30 Dec 2013, 04:41
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