# How many five letter words can be formed from the English alphabet that contain $2$ different consonants and $3$ different vowels? [closed]

The English alphabet has $26$ letters, of which $5$ are vowels.

(a) How many five letter "words" containing $2$ different consonants and $3$ different vowels can be formed?

(b) How many of these "words" begin with "b" and end in "a"?

I have done part a $21C2 \cdot 5C3 \cdot 5! = 252000$. Not sure how to solve part b.

## closed as off-topic by user296602, Namaste, mlc, Hurkyl, Kevin LongMar 26 '18 at 20:07

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Namaste, mlc, Hurkyl, Kevin Long
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• Lots, and then less. What have you tried and where are you encountering difficulty here? This is not a do-my-homework site; please edit accordingy. – user296602 Mar 26 '18 at 17:32

How many five letter words can be formed from the English alphabet that contain $2$ different consonants and $3$ different vowels?
How many of these words begin with $b$ and end with $a$?
We have to choose one of the other $20$ consonants, two of the other four vowels, and then arrange the three chosen letters in the three spaces between $b$ and $a$.
$$\binom{20}{1}\binom{4}{2}3!$$