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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.

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

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

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    $\begingroup$ 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. $\endgroup$ – user296602 Mar 26 '18 at 17:32
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How many five letter words can be formed from the English alphabet that contain $2$ different consonants and $3$ different vowels?

Your answer is correct.

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 $a$.

$$\binom{20}{1}\binom{4}{2}3!$$

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20C1*4C2*3! Fix the positions of b in the beginning and a at the end. Now you have 20 consonants and 4 vowels and 3 positions to fill.

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