How many words of 2 distinct vowels and 3 distinct consonant

Question

How many words of 2 distinct vowels and 3 distinct consonants can be made using the English Alphabet?

my approach was

C 5 2 * C 21 3 / C 26 5

PLz correct me I am wrong

ranga41 · Answer

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...

goforsriram · Answer

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!

goforsriram · Answer

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!

jlgdr · Answer

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

suramya26 · Answer

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

Senthil1981 · Answer

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! .

hdwnkr · Answer

So, we are given 2 distinct vowels and 3 distinct consonants is just to confuse and bring in the identical concept. It might just be a question of forming number of words using 5 different alphabets. 5!

But, if we are also select the 2 distinct vowels and 3 distinct consonants, the selection for vowels would be 5C2 and consonants would be 21C3. And then these would have to be arranged i.e. 5C2 * 21C3 * 5!?

Bunuel  pls help

rohit8865 · Answer

We have not been provided any marked vowels/consonants
rather we need to select any from all those
Also we can form any words either having any meaning or meaningless

thus on first step we have to select ,than on second step arrange them..

so your later consideration must be correct one..

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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

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