Question

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

• A. 5780
• B. 2890
• C. 5440
• D. 2720

Answer 1

Answer: (A)

5780

Answer 2

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 $=(17)^{2} \cdot 20=5780$.