Quick Combinatorics Question

[clıppy]

I've got this question that I just can't figure out:

There are 5 vowels and 21 consonants in the English alphabet. How many different four-letter 'words' can be formed that contain two different vowels and two different consonants?

The answer is apparently 11,025 but i got 50,400, can anyone explain this to me?

[b^3]

These 'words' can have the vowels and consonants in any order.
So that is we can have (where v is a vowel and c is a consonant)








Now the number of ways we can arrange the first row is

We minus 1 the second time because we can't use the same vowel or the sam consonant twice.
If we do the same for the second row we get


So as we can see all the rows will have options, and we have six rows.
So the total number of 'words' that can be formed is

Thats probably a more intutive way of doing it, but it still gets the answer

[clıppy]

So the answer is 50,400 not 11,025 making the back of the book wrong. Thanks b^3

[b^3]

So the answer is 50,400 not 11,025 making the back of the book wrong. Thanks b^3

Oh wait... I read what you said wrong before... give me a minute, I'm probably wrong too...... (still waking up...)



EDIT: I think it looks right.... unless someone else can find something wrong with it.

(also we have another westsider on AN! )

[clıppy]

Haha that's alright

[TrueTears]

I'll let you think about why