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  4. With 17 consonants and 5 vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is

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Q. With $17$ consonants and $5$ vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is

BITSATBITSAT 2010

Solution:

The two letters, the first and the last of the four lettered word can be chosen in $(17)^{2}$ ways, as repetition is allowed for consonants.
The two vowels in the middle are distinct so that the number of ways of filling up the two places is ${ }^{5} P_{2}=20$.
The no. of different words $=(17)^{2} \cdot 20=5780$.