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

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

Tardigrade Admin · Accepted Answer

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

.

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

5780

2890

5440

2720

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 5P2​=20. The no. of different words =(17)2⋅20=5780.

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