How many five letter words containing 3 vowels and 2 consonants can be formed using the letters of the word EQUATION so that the two consonants occur together?

Options

A. 720
B. 1440
C. 240
D. 480

Answer

B

Explanation

There are 5 vowels and 3 consonants in the word 'EQUATION'. Three vowels out of 5 and 2 consonants out of 3 can be chosen in `""^(5)C_(3)xx""^(3)C_(2)` ways. So, there are `""^(5)C_(3)xx""^(3)C_(2)` groups each containing 3 consonants and two vowels. Now, each group contains 5 letters which are to be arranged in such a way that 2 consonats occur together. Considering 2 consonants as one letter we have 4 letters which can be arranged in 4! ways. But two consonants can be put together in 2! ways. Therefore, 5 letters in each group can be arranged in `4!xx2!` ways.
`:.` Required number of words `=(""^(5)C_(3)xx""^(3)C_(2))xx4!xx2!=1440`.